%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : PRO025^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:28:08 AM UTC 2026
% Result : Theorem 20.81s 4.57s
% Output : Refutation 20.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : PRO025^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.30 % Computer : n025.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8042.1875MB
% 0.12/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Tue Feb 24 11:29:42 EST 2026
% 0.12/0.30 % CPUTime :
% 0.12/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.39 ---- Original DTF file ---
% 0.16/0.39 thf(spec,logic,$$dhol).
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 % File : PRO025^1 : TPTP v9.2.1. Released v7.0.0.
% 0.16/0.39 % Domain : Processes
% 0.16/0.39 % Problem : Process algebra 199
% 0.16/0.39 % Version : [Bla16] axioms : Especial.
% 0.16/0.39 % English :
% 0.16/0.39
% 0.16/0.39 % Refs : [BH+14] Blanchette et al. (2014), Truly Modular (Co)datatypes
% 0.16/0.39 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.16/0.39 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.16/0.39 % Source : [Bla16]
% 0.16/0.39 % Names : process__199.p [Bla16]
% 0.16/0.39
% 0.16/0.39 % Status : Theorem
% 0.16/0.39 % Rating : 0.33 v9.1.0, 0.00 v8.1.0, 0.25 v7.5.0, 0.00 v7.2.0, 0.25 v7.1.0
% 0.16/0.39 % Syntax : Number of formulae : 325 ( 143 unt; 66 typ; 0 def)
% 0.16/0.39 % Number of atoms : 887 ( 371 equ; 0 cnn)
% 0.16/0.39 % Maximal formula atoms : 31 ( 3 avg)
% 0.16/0.39 % Number of connectives : 8625 ( 169 ~; 10 |; 49 &;8017 @)
% 0.16/0.39 % ( 0 <=>; 380 =>; 0 <=; 0 <~>)
% 0.16/0.39 % Maximal formula depth : 31 ( 12 avg)
% 0.16/0.39 % Number of types : 3 ( 2 usr)
% 0.16/0.39 % Number of type conns : 1385 (1385 >; 0 *; 0 +; 0 <<)
% 0.16/0.39 % Number of symbols : 67 ( 64 usr; 8 con; 0-14 aty)
% 0.16/0.39 % Number of variables : 2035 ( 238 ^;1668 !; 23 ?;2035 :)
% 0.16/0.39 % ( 106 !>; 0 ?*; 0 @-; 0 @+)
% 0.16/0.39 % SPC : TH1_THM_EQU_NAR
% 0.16/0.39
% 0.16/0.39 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.16/0.39 % 2016-07-13 14:40:06.073
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 %----Could-be-implicit typings (7)
% 0.16/0.39 thf(ty_t_Process__Mirabelle__xovoopgpgi_Oprocess__term,type,
% 0.16/0.39 proces554692349s_term: $tType > $tType > $tType ).
% 0.16/0.39
% 0.16/0.39 thf(ty_t_Process__Mirabelle__xovoopgpgi_Oprocess,type,
% 0.16/0.39 proces634752977rocess: $tType > $tType ).
% 0.16/0.39
% 0.16/0.39 thf(ty_t_Product__Type_Oprod,type,
% 0.16/0.39 product_prod: $tType > $tType > $tType ).
% 0.16/0.39
% 0.16/0.39 thf(ty_t_Set_Oset,type,
% 0.16/0.39 set: $tType > $tType ).
% 0.16/0.39
% 0.16/0.39 thf(ty_t_itself,type,
% 0.16/0.39 itself: $tType > $tType ).
% 0.16/0.39
% 0.16/0.39 thf(ty_tf_b,type,
% 0.16/0.39 b: $tType ).
% 0.16/0.39
% 0.16/0.39 thf(ty_tf_a,type,
% 0.16/0.39 a: $tType ).
% 0.16/0.39
% 0.16/0.39 %----Explicit typings (59)
% 0.16/0.39 thf(sy_c_BNF__Def_Orel__fun,type,
% 0.16/0.39 bNF_rel_fun:
% 0.16/0.39 !>[A: $tType,C: $tType,B: $tType,D: $tType] : ( ( A > C > $o ) > ( B > D > $o ) > ( A > B ) > ( C > D ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_HOL_Oundefined,type,
% 0.16/0.39 undefined:
% 0.16/0.39 !>[A: $tType] : A ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_If,type,
% 0.16/0.39 if:
% 0.16/0.39 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH1,type,
% 0.16/0.39 proces1239275103le_CH1:
% 0.16/0.39 !>[A: $tType,B: $tType] : ( ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > ( proces554692349s_term @ B @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH1__rel,type,
% 0.16/0.39 proces1869379930H1_rel:
% 0.16/0.39 !>[A: $tType,B: $tType] : ( ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH2,type,
% 0.16/0.39 proces1239275104le_CH2:
% 0.16/0.39 !>[A: $tType,B: $tType] : ( ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > ( proces554692349s_term @ B @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH2__rel,type,
% 0.16/0.39 proces93903513H2_rel:
% 0.16/0.39 !>[A: $tType,B: $tType] : ( ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCONT,type,
% 0.16/0.39 proces126235999e_CONT:
% 0.16/0.39 !>[A: $tType,B: $tType] : ( ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > ( proces554692349s_term @ B @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCONT__rel,type,
% 0.16/0.39 proces1004198490NT_rel:
% 0.16/0.39 !>[A: $tType,B: $tType] : ( ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Process__Mirabelle__xovoopgpgi_OPREF,type,
% 0.16/0.39 proces1708129104e_PREF:
% 0.16/0.39 !>[A: $tType,B: $tType,C: $tType] : ( ( A > ( proces554692349s_term @ B @ C ) ) > ( proces554692349s_term @ B @ A ) > B ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Process__Mirabelle__xovoopgpgi_OPREF__rel,type,
% 0.16/0.39 proces527360425EF_rel:
% 0.16/0.39 !>[A: $tType,B: $tType,C: $tType] : ( ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) > ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oguarded,type,
% 0.16/0.39 proces1121166967uarded:
% 0.16/0.39 !>[A: $tType,B: $tType,C: $tType] : ( ( A > ( proces554692349s_term @ B @ C ) ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Process__Mirabelle__xovoopgpgi_OisACT,type,
% 0.16/0.39 proces687458811_isACT:
% 0.16/0.39 !>[A: $tType,B: $tType,C: $tType,D: $tType] : ( ( A > ( proces554692349s_term @ B @ C ) ) > ( proces554692349s_term @ D @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Process__Mirabelle__xovoopgpgi_OisACT__rel,type,
% 0.16/0.39 proces896239806CT_rel:
% 0.16/0.39 !>[A: $tType,B: $tType,C: $tType,D: $tType] : ( ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) > ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OAction,type,
% 0.16/0.39 proces1525233512Action:
% 0.16/0.39 !>[A: $tType] : ( A > ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OChoice,type,
% 0.16/0.39 proces1915862579Choice:
% 0.16/0.39 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Ocase__process,type,
% 0.16/0.39 proces1406508781rocess:
% 0.16/0.39 !>[A: $tType,B: $tType] : ( ( A > ( proces634752977rocess @ A ) > B ) > ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B ) > ( proces634752977rocess @ A ) > B ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Och1Of,type,
% 0.16/0.39 proces979765041_ch1Of:
% 0.16/0.39 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Och2Of,type,
% 0.16/0.39 proces988026546_ch2Of:
% 0.16/0.39 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OcontOf,type,
% 0.16/0.39 proces1778668539contOf:
% 0.16/0.39 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Ocorec__process,type,
% 0.16/0.39 proces894737309rocess:
% 0.16/0.39 !>[C: $tType,A: $tType] : ( ( C > $o ) > ( C > A ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OisAction,type,
% 0.16/0.39 proces10484146Action:
% 0.16/0.39 !>[A: $tType] : ( ( proces634752977rocess @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OisChoice,type,
% 0.16/0.39 proces401113213Choice:
% 0.16/0.39 !>[A: $tType] : ( ( proces634752977rocess @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Omap__process,type,
% 0.16/0.39 proces370407749rocess:
% 0.16/0.39 !>[A: $tType,Aa: $tType] : ( ( A > Aa ) > ( proces634752977rocess @ A ) > ( proces634752977rocess @ Aa ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Opred__process,type,
% 0.16/0.39 proces1205983068rocess:
% 0.16/0.39 !>[A: $tType] : ( ( A > $o ) > ( proces634752977rocess @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OprefOf,type,
% 0.16/0.39 proces745025900prefOf:
% 0.16/0.39 !>[A: $tType] : ( ( proces634752977rocess @ A ) > A ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Orel__process,type,
% 0.16/0.39 proces749077512rocess:
% 0.16/0.39 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( proces634752977rocess @ A ) > ( proces634752977rocess @ B ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OACT,type,
% 0.16/0.39 proces1454156180ss_ACT:
% 0.16/0.39 !>[A: $tType,Pvar: $tType] : ( A > ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OCH,type,
% 0.16/0.39 proces89589571ess_CH:
% 0.16/0.39 !>[A: $tType,Pvar: $tType] : ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OPROC,type,
% 0.16/0.39 proces1062592052s_PROC:
% 0.16/0.39 !>[A: $tType,Pvar: $tType] : ( ( proces634752977rocess @ A ) > ( proces554692349s_term @ A @ Pvar ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OVAR,type,
% 0.16/0.39 proces1627516585ss_VAR:
% 0.16/0.39 !>[Pvar: $tType,A: $tType] : ( Pvar > ( proces554692349s_term @ A @ Pvar ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Ocase__process__term,type,
% 0.16/0.39 proces460752237s_term:
% 0.16/0.39 !>[Pvar: $tType,B: $tType,A: $tType] : ( ( Pvar > B ) > ( ( proces634752977rocess @ A ) > B ) > ( A > ( proces554692349s_term @ A @ Pvar ) > B ) > ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B ) > ( proces554692349s_term @ A @ Pvar ) > B ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Omap__process__term,type,
% 0.16/0.39 proces224683037s_term:
% 0.16/0.39 !>[A: $tType,Aa: $tType,Pvar: $tType,Pvara: $tType] : ( ( A > Aa ) > ( Pvar > Pvara ) > ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ Aa @ Pvara ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Opred__process__term,type,
% 0.16/0.39 proces2118920028s_term:
% 0.16/0.39 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( B > $o ) > ( proces554692349s_term @ A @ B ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Orec__process__term,type,
% 0.16/0.39 proces2117273769s_term:
% 0.16/0.39 !>[Pvar: $tType,D: $tType,A: $tType] : ( ( Pvar > D ) > ( ( proces634752977rocess @ A ) > D ) > ( A > ( proces554692349s_term @ A @ Pvar ) > D > D ) > ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Orel__process__term,type,
% 0.16/0.39 proces2029722208s_term:
% 0.16/0.39 !>[A: $tType,C: $tType,B: $tType,D: $tType] : ( ( A > C > $o ) > ( B > D > $o ) > ( proces554692349s_term @ A @ B ) > ( proces554692349s_term @ C @ D ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Oset2__process__term,type,
% 0.16/0.39 proces1493547885s_term:
% 0.16/0.39 !>[A: $tType,Pvar: $tType] : ( ( proces554692349s_term @ A @ Pvar ) > ( set @ Pvar ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Process__Mirabelle__xovoopgpgi_Osolution,type,
% 0.16/0.39 proces1652378886lution:
% 0.16/0.39 !>[A: $tType,B: $tType] : ( ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > ( proces634752977rocess @ B ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Product__Type_OPair,type,
% 0.16/0.39 product_Pair:
% 0.16/0.39 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Product__Type_Ocurry,type,
% 0.16/0.39 product_curry:
% 0.16/0.39 !>[A: $tType,B: $tType,C: $tType] : ( ( ( product_prod @ A @ B ) > C ) > A > B > C ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 0.16/0.39 produc2004651681e_prod:
% 0.16/0.39 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 0.16/0.39 product_rec_prod:
% 0.16/0.39 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Pure_Otype,type,
% 0.16/0.39 type:
% 0.16/0.39 !>[A: $tType] : ( itself @ A ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Relation_Oinv__image,type,
% 0.16/0.39 inv_image:
% 0.16/0.39 !>[B: $tType,A: $tType] : ( ( set @ ( product_prod @ B @ B ) ) > ( A > B ) > ( set @ ( product_prod @ A @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Set_OCollect,type,
% 0.16/0.39 collect:
% 0.16/0.39 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Wellfounded_Oacc,type,
% 0.16/0.39 acc:
% 0.16/0.39 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Wellfounded_Oaccp,type,
% 0.16/0.39 accp:
% 0.16/0.39 !>[A: $tType] : ( ( A > A > $o ) > A > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Wellfounded_Olex__prod,type,
% 0.16/0.39 lex_prod:
% 0.16/0.39 !>[A: $tType,B: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ B @ B ) ) > ( set @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Wfrec_Oadm__wf,type,
% 0.16/0.39 adm_wf:
% 0.16/0.39 !>[A: $tType,B: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( ( A > B ) > A > B ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Wfrec_Ocut,type,
% 0.16/0.39 cut:
% 0.16/0.39 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ ( product_prod @ A @ A ) ) > A > A > B ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Wfrec_Osame__fst,type,
% 0.16/0.39 same_fst:
% 0.16/0.39 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( A > ( set @ ( product_prod @ B @ B ) ) ) > ( set @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_member,type,
% 0.16/0.39 member:
% 0.16/0.39 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_v_a_H____,type,
% 0.16/0.39 a2: a ).
% 0.16/0.39
% 0.16/0.39 thf(sy_v_a____,type,
% 0.16/0.39 a3: a ).
% 0.16/0.39
% 0.16/0.39 thf(sy_v_p,type,
% 0.16/0.39 p: proces634752977rocess @ a ).
% 0.16/0.39
% 0.16/0.39 thf(sy_v_p_H____,type,
% 0.16/0.39 p2: proces634752977rocess @ a ).
% 0.16/0.39
% 0.16/0.39 thf(sy_v_pa____,type,
% 0.16/0.39 pa: proces634752977rocess @ a ).
% 0.16/0.39
% 0.16/0.39 thf(sy_v_q____,type,
% 0.16/0.39 q: proces634752977rocess @ a ).
% 0.16/0.39
% 0.16/0.39 thf(sy_v_sys,type,
% 0.16/0.39 sys: b > ( proces554692349s_term @ a @ b ) ).
% 0.16/0.39
% 0.16/0.39 %----Relevant facts (255)
% 0.16/0.39 thf(fact_0__092_060open_062q_A_061_Asolution_Asys_A_IPROC_Ap_J_092_060close_062,axiom,
% 0.16/0.39 ( q
% 0.16/0.39 = ( proces1652378886lution @ b @ a @ sys @ ( proces1062592052s_PROC @ a @ b @ p ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % \<open>q = solution sys (PROC p)\<close>
% 0.16/0.39 thf(fact_1_process__term_Oinject_I2_J,axiom,
% 0.16/0.39 ! [Pvar: $tType,A: $tType,X2: proces634752977rocess @ A,Y2: proces634752977rocess @ A] :
% 0.16/0.39 ( ( ( proces1062592052s_PROC @ A @ Pvar @ X2 )
% 0.16/0.39 = ( proces1062592052s_PROC @ A @ Pvar @ Y2 ) )
% 0.16/0.39 = ( X2 = Y2 ) ) ).
% 0.16/0.39
% 0.16/0.39 % process_term.inject(2)
% 0.16/0.39 thf(fact_2_Action,axiom,
% 0.16/0.39 ( ( proces1525233512Action @ a @ a2 @ p2 )
% 0.16/0.39 = ( proces1652378886lution @ b @ a @ sys @ ( proces1062592052s_PROC @ a @ b @ ( proces1525233512Action @ a @ a3 @ pa ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % Action
% 0.16/0.39 thf(fact_3__C0_C,axiom,
% 0.16/0.39 proces687458811_isACT @ b @ a @ b @ a @ sys @ ( proces1062592052s_PROC @ a @ b @ ( proces1525233512Action @ a @ a3 @ pa ) ) ).
% 0.16/0.39
% 0.16/0.39 % "0"
% 0.16/0.39 thf(fact_4__092_060open_062solution_Asys_A_IPROC_A_IAction_Aa_Ap_J_J_A_061_AAction_A_IPREF_Asys_A_IPROC_A_IAction_Aa_Ap_J_J_J_A_Isolution_Asys_A_ICONT_Asys_A_IPROC_A_IAction_Aa_Ap_J_J_J_J_092_060close_062,axiom,
% 0.16/0.39 ( ( proces1652378886lution @ b @ a @ sys @ ( proces1062592052s_PROC @ a @ b @ ( proces1525233512Action @ a @ a3 @ pa ) ) )
% 0.16/0.39 = ( proces1525233512Action @ a @ ( proces1708129104e_PREF @ b @ a @ b @ sys @ ( proces1062592052s_PROC @ a @ b @ ( proces1525233512Action @ a @ a3 @ pa ) ) ) @ ( proces1652378886lution @ b @ a @ sys @ ( proces126235999e_CONT @ b @ a @ sys @ ( proces1062592052s_PROC @ a @ b @ ( proces1525233512Action @ a @ a3 @ pa ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % \<open>solution sys (PROC (Action a p)) = Action (PREF sys (PROC (Action a p))) (solution sys (CONT sys (PROC (Action a p))))\<close>
% 0.16/0.39 thf(fact_5_process__term_Osimps_I22_J,axiom,
% 0.16/0.39 ! [Pvar: $tType,D: $tType,A: $tType,F1: Pvar > D,F2: ( proces634752977rocess @ A ) > D,F3: A > ( proces554692349s_term @ A @ Pvar ) > D > D,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D,X2: proces634752977rocess @ A] :
% 0.16/0.39 ( ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) )
% 0.16/0.39 = ( F2 @ X2 ) ) ).
% 0.16/0.39
% 0.16/0.39 % process_term.simps(22)
% 0.16/0.39 thf(fact_6_process__term_Osimps_I18_J,axiom,
% 0.16/0.39 ! [Pvar: $tType,B: $tType,A: $tType,F1: Pvar > B,F2: ( proces634752977rocess @ A ) > B,F3: A > ( proces554692349s_term @ A @ Pvar ) > B,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B,X2: proces634752977rocess @ A] :
% 0.16/0.39 ( ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) )
% 0.16/0.39 = ( F2 @ X2 ) ) ).
% 0.16/0.39
% 0.16/0.39 % process_term.simps(18)
% 0.16/0.39 thf(fact_7_process__term_Odistinct_I7_J,axiom,
% 0.16/0.39 ! [Pvar: $tType,A: $tType,X2: proces634752977rocess @ A,X31: A,X32: proces554692349s_term @ A @ Pvar] :
% 0.16/0.39 ( ( proces1062592052s_PROC @ A @ Pvar @ X2 )
% 0.16/0.39 != ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) ) ).
% 0.16/0.39
% 0.16/0.39 % process_term.distinct(7)
% 0.16/0.39 thf(fact_8_process__term_Odistinct_I9_J,axiom,
% 0.16/0.39 ! [Pvar: $tType,A: $tType,X2: proces634752977rocess @ A,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
% 0.16/0.39 ( ( proces1062592052s_PROC @ A @ Pvar @ X2 )
% 0.16/0.39 != ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) ) ).
% 0.16/0.39
% 0.16/0.39 % process_term.distinct(9)
% 0.16/0.39 thf(fact_9_process__term_Odistinct_I1_J,axiom,
% 0.16/0.39 ! [Pvar: $tType,A: $tType,X1: Pvar,X2: proces634752977rocess @ A] :
% 0.16/0.39 ( ( proces1627516585ss_VAR @ Pvar @ A @ X1 )
% 0.16/0.39 != ( proces1062592052s_PROC @ A @ Pvar @ X2 ) ) ).
% 0.16/0.39
% 0.16/0.39 % process_term.distinct(1)
% 0.16/0.39 thf(fact_10_process_Ocase__distrib,axiom,
% 0.16/0.39 ! [B: $tType,C: $tType,A: $tType,H: B > C,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process: proces634752977rocess @ A] :
% 0.16/0.39 ( ( H @ ( proces1406508781rocess @ A @ B @ F1 @ F2 @ Process ) )
% 0.16/0.39 = ( proces1406508781rocess @ A @ C
% 0.16/0.39 @ ^ [X12: A,X22: proces634752977rocess @ A] : ( H @ ( F1 @ X12 @ X22 ) )
% 0.16/0.39 @ ^ [X12: proces634752977rocess @ A,X22: proces634752977rocess @ A] : ( H @ ( F2 @ X12 @ X22 ) )
% 0.16/0.39 @ Process ) ) ).
% 0.16/0.39
% 0.16/0.39 % process.case_distrib
% 0.16/0.39 thf(fact_11_process__term_Ocase__distrib,axiom,
% 0.16/0.39 ! [B: $tType,C: $tType,Pvar: $tType,A: $tType,H: B > C,F1: Pvar > B,F2: ( proces634752977rocess @ A ) > B,F3: A > ( proces554692349s_term @ A @ Pvar ) > B,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B,Process_term: proces554692349s_term @ A @ Pvar] :
% 0.16/0.39 ( ( H @ ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ Process_term ) )
% 0.16/0.39 = ( proces460752237s_term @ Pvar @ C @ A
% 0.16/0.39 @ ^ [X: Pvar] : ( H @ ( F1 @ X ) )
% 0.16/0.39 @ ^ [X: proces634752977rocess @ A] : ( H @ ( F2 @ X ) )
% 0.16/0.39 @ ^ [X12: A,X22: proces554692349s_term @ A @ Pvar] : ( H @ ( F3 @ X12 @ X22 ) )
% 0.16/0.39 @ ^ [X12: proces554692349s_term @ A @ Pvar,X22: proces554692349s_term @ A @ Pvar] : ( H @ ( F4 @ X12 @ X22 ) )
% 0.16/0.39 @ Process_term ) ) ).
% 0.16/0.39
% 0.16/0.39 % process_term.case_distrib
% 0.16/0.39 thf(fact_12_solution__VAR,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X3: A] :
% 0.16/0.39 ( ( proces1121166967uarded @ A @ B @ A @ Sys )
% 0.16/0.39 => ( ( proces1652378886lution @ A @ B @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X3 ) )
% 0.16/0.39 = ( proces1652378886lution @ A @ B @ Sys @ ( Sys @ X3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % solution_VAR
% 0.16/0.39 thf(fact_13_PREF_Osimps_I2_J,axiom,
% 0.16/0.39 ! [A: $tType,C: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ C ),P: proces634752977rocess @ B] :
% 0.16/0.39 ( ( proces1708129104e_PREF @ A @ B @ C @ Sys @ ( proces1062592052s_PROC @ B @ A @ P ) )
% 0.16/0.39 = ( proces745025900prefOf @ B @ P ) ) ).
% 0.16/0.39
% 0.16/0.39 % PREF.simps(2)
% 0.16/0.39 thf(fact_14_process__term_Opred__inject_I2_J,axiom,
% 0.16/0.39 ! [Pvar: $tType,A: $tType,P1: A > $o,P2: Pvar > $o,A2: proces634752977rocess @ A] :
% 0.16/0.39 ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ ( proces1062592052s_PROC @ A @ Pvar @ A2 ) )
% 0.16/0.39 = ( proces1205983068rocess @ A @ P1 @ A2 ) ) ).
% 0.16/0.39
% 0.16/0.39 % process_term.pred_inject(2)
% 0.16/0.39 thf(fact_15_process__term_Oinject_I1_J,axiom,
% 0.16/0.39 ! [A: $tType,Pvar: $tType,X1: Pvar,Y1: Pvar] :
% 0.16/0.39 ( ( ( proces1627516585ss_VAR @ Pvar @ A @ X1 )
% 0.16/0.39 = ( proces1627516585ss_VAR @ Pvar @ A @ Y1 ) )
% 0.16/0.39 = ( X1 = Y1 ) ) ).
% 0.16/0.39
% 0.16/0.39 % process_term.inject(1)
% 0.16/0.39 thf(fact_16_process__term_Oinject_I4_J,axiom,
% 0.16/0.39 ! [Pvar: $tType,A: $tType,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar,Y41: proces554692349s_term @ A @ Pvar,Y42: proces554692349s_term @ A @ Pvar] :
% 0.16/0.39 ( ( ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 )
% 0.16/0.39 = ( proces89589571ess_CH @ A @ Pvar @ Y41 @ Y42 ) )
% 0.16/0.39 = ( ( X41 = Y41 )
% 0.16/0.39 & ( X42 = Y42 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % process_term.inject(4)
% 0.16/0.39 thf(fact_17_process__term_Oinject_I3_J,axiom,
% 0.16/0.39 ! [Pvar: $tType,A: $tType,X31: A,X32: proces554692349s_term @ A @ Pvar,Y31: A,Y32: proces554692349s_term @ A @ Pvar] :
% 0.16/0.39 ( ( ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 )
% 0.16/0.39 = ( proces1454156180ss_ACT @ A @ Pvar @ Y31 @ Y32 ) )
% 0.16/0.39 = ( ( X31 = Y31 )
% 0.16/0.39 & ( X32 = Y32 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % process_term.inject(3)
% 0.16/0.39 thf(fact_18_process_Oinject_I1_J,axiom,
% 0.16/0.39 ! [A: $tType,X11: A,X122: proces634752977rocess @ A,Y11: A,Y12: proces634752977rocess @ A] :
% 0.16/0.39 ( ( ( proces1525233512Action @ A @ X11 @ X122 )
% 0.16/0.39 = ( proces1525233512Action @ A @ Y11 @ Y12 ) )
% 0.16/0.39 = ( ( X11 = Y11 )
% 0.16/0.39 & ( X122 = Y12 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % process.inject(1)
% 0.16/0.39 thf(fact_19_process__term_Opred__inject_I1_J,axiom,
% 0.16/0.39 ! [A: $tType,Pvar: $tType,P1: A > $o,P2: Pvar > $o,A2: Pvar] :
% 0.16/0.39 ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ ( proces1627516585ss_VAR @ Pvar @ A @ A2 ) )
% 0.16/0.39 = ( P2 @ A2 ) ) ).
% 0.16/0.39
% 0.16/0.39 % process_term.pred_inject(1)
% 0.16/0.39 thf(fact_20_process__term_Opred__inject_I4_J,axiom,
% 0.16/0.39 ! [Pvar: $tType,A: $tType,P1: A > $o,P2: Pvar > $o,A2: proces554692349s_term @ A @ Pvar,Aa2: proces554692349s_term @ A @ Pvar] :
% 0.16/0.39 ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ ( proces89589571ess_CH @ A @ Pvar @ A2 @ Aa2 ) )
% 0.16/0.39 = ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ A2 )
% 0.16/0.39 & ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ Aa2 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % process_term.pred_inject(4)
% 0.16/0.39 thf(fact_21_process__term_Opred__inject_I3_J,axiom,
% 0.16/0.39 ! [Pvar: $tType,A: $tType,P1: A > $o,P2: Pvar > $o,A2: A,Aa2: proces554692349s_term @ A @ Pvar] :
% 0.16/0.39 ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ ( proces1454156180ss_ACT @ A @ Pvar @ A2 @ Aa2 ) )
% 0.16/0.39 = ( ( P1 @ A2 )
% 0.16/0.39 & ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ Aa2 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % process_term.pred_inject(3)
% 0.16/0.39 thf(fact_22_process_Opred__inject_I1_J,axiom,
% 0.16/0.39 ! [A: $tType,P3: A > $o,A2: A,Aa2: proces634752977rocess @ A] :
% 0.16/0.39 ( ( proces1205983068rocess @ A @ P3 @ ( proces1525233512Action @ A @ A2 @ Aa2 ) )
% 0.16/0.39 = ( ( P3 @ A2 )
% 0.16/0.39 & ( proces1205983068rocess @ A @ P3 @ Aa2 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % process.pred_inject(1)
% 0.16/0.39 thf(fact_23_CONT_Osimps_I3_J,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),A2: B,T2: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( ( proces126235999e_CONT @ A @ B @ Sys @ ( proces1454156180ss_ACT @ B @ A @ A2 @ T2 ) )
% 0.16/0.39 = T2 ) ).
% 0.16/0.39
% 0.16/0.39 % CONT.simps(3)
% 0.16/0.39 thf(fact_24_PREF_Osimps_I3_J,axiom,
% 0.16/0.39 ! [A: $tType,C: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ C ),A2: B,T2: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( ( proces1708129104e_PREF @ A @ B @ C @ Sys @ ( proces1454156180ss_ACT @ B @ A @ A2 @ T2 ) )
% 0.16/0.39 = A2 ) ).
% 0.16/0.39
% 0.16/0.39 % PREF.simps(3)
% 0.16/0.39 thf(fact_25_isACT_Osimps_I4_J,axiom,
% 0.16/0.39 ! [B: $tType,C: $tType,A: $tType,D: $tType,Sys: A > ( proces554692349s_term @ B @ C ),T1: proces554692349s_term @ D @ A,T22: proces554692349s_term @ D @ A] :
% 0.16/0.39 ~ ( proces687458811_isACT @ A @ B @ C @ D @ Sys @ ( proces89589571ess_CH @ D @ A @ T1 @ T22 ) ) ).
% 0.16/0.39
% 0.16/0.39 % isACT.simps(4)
% 0.16/0.39 thf(fact_26_isACT_Osimps_I3_J,axiom,
% 0.16/0.39 ! [B: $tType,C: $tType,A: $tType,D: $tType,Sys: A > ( proces554692349s_term @ B @ C ),A2: D,T2: proces554692349s_term @ D @ A] : ( proces687458811_isACT @ A @ B @ C @ D @ Sys @ ( proces1454156180ss_ACT @ D @ A @ A2 @ T2 ) ) ).
% 0.16/0.39
% 0.16/0.39 % isACT.simps(3)
% 0.16/0.39 thf(fact_27_process_Osel_I1_J,axiom,
% 0.16/0.39 ! [A: $tType,X11: A,X122: proces634752977rocess @ A] :
% 0.16/0.39 ( ( proces745025900prefOf @ A @ ( proces1525233512Action @ A @ X11 @ X122 ) )
% 0.16/0.39 = X11 ) ).
% 0.16/0.39
% 0.16/0.39 % process.sel(1)
% 0.16/0.39 thf(fact_28_solution_Octr_I1_J,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 0.16/0.39 => ( ( proces1652378886lution @ A @ B @ Sys @ T2 )
% 0.16/0.39 = ( proces1525233512Action @ B @ ( proces1708129104e_PREF @ A @ B @ A @ Sys @ T2 ) @ ( proces1652378886lution @ A @ B @ Sys @ ( proces126235999e_CONT @ A @ B @ Sys @ T2 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % solution.ctr(1)
% 0.16/0.39 thf(fact_29_process_Osimps_I5_J,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,X11: A,X122: proces634752977rocess @ A] :
% 0.16/0.39 ( ( proces1406508781rocess @ A @ B @ F1 @ F2 @ ( proces1525233512Action @ A @ X11 @ X122 ) )
% 0.16/0.39 = ( F1 @ X11 @ X122 ) ) ).
% 0.16/0.39
% 0.16/0.39 % process.simps(5)
% 0.16/0.39 thf(fact_30_process__term_Osimps_I24_J,axiom,
% 0.16/0.39 ! [D: $tType,Pvar: $tType,A: $tType,F1: Pvar > D,F2: ( proces634752977rocess @ A ) > D,F3: A > ( proces554692349s_term @ A @ Pvar ) > D > D,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
% 0.16/0.39 ( ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) )
% 0.16/0.39 = ( F4 @ X41 @ X42 @ ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ X41 ) @ ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ X42 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % process_term.simps(24)
% 0.16/0.39 thf(fact_31_process__term_Osimps_I23_J,axiom,
% 0.16/0.39 ! [D: $tType,Pvar: $tType,A: $tType,F1: Pvar > D,F2: ( proces634752977rocess @ A ) > D,F3: A > ( proces554692349s_term @ A @ Pvar ) > D > D,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D,X31: A,X32: proces554692349s_term @ A @ Pvar] :
% 0.16/0.39 ( ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) )
% 0.16/0.39 = ( F3 @ X31 @ X32 @ ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ X32 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % process_term.simps(23)
% 0.16/0.39 thf(fact_32_process__term_Osimps_I21_J,axiom,
% 0.16/0.39 ! [A: $tType,D: $tType,Pvar: $tType,F1: Pvar > D,F2: ( proces634752977rocess @ A ) > D,F3: A > ( proces554692349s_term @ A @ Pvar ) > D > D,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D,X1: Pvar] :
% 0.16/0.39 ( ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) )
% 0.16/0.39 = ( F1 @ X1 ) ) ).
% 0.16/0.39
% 0.16/0.39 % process_term.simps(21)
% 0.16/0.39 thf(fact_33_process__term_Osimps_I20_J,axiom,
% 0.16/0.39 ! [B: $tType,Pvar: $tType,A: $tType,F1: Pvar > B,F2: ( proces634752977rocess @ A ) > B,F3: A > ( proces554692349s_term @ A @ Pvar ) > B,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
% 0.16/0.39 ( ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) )
% 0.16/0.39 = ( F4 @ X41 @ X42 ) ) ).
% 0.16/0.39
% 0.16/0.39 % process_term.simps(20)
% 0.16/0.39 thf(fact_34_process__term_Osimps_I19_J,axiom,
% 0.16/0.39 ! [B: $tType,Pvar: $tType,A: $tType,F1: Pvar > B,F2: ( proces634752977rocess @ A ) > B,F3: A > ( proces554692349s_term @ A @ Pvar ) > B,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B,X31: A,X32: proces554692349s_term @ A @ Pvar] :
% 0.16/0.39 ( ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) )
% 0.16/0.39 = ( F3 @ X31 @ X32 ) ) ).
% 0.16/0.39
% 0.16/0.39 % process_term.simps(19)
% 0.16/0.39 thf(fact_35_process__term_Osimps_I17_J,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,Pvar: $tType,F1: Pvar > B,F2: ( proces634752977rocess @ A ) > B,F3: A > ( proces554692349s_term @ A @ Pvar ) > B,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B,X1: Pvar] :
% 0.16/0.39 ( ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) )
% 0.16/0.39 = ( F1 @ X1 ) ) ).
% 0.16/0.39
% 0.16/0.39 % process_term.simps(17)
% 0.16/0.39 thf(fact_36_process__term_Odistinct_I11_J,axiom,
% 0.16/0.39 ! [Pvar: $tType,A: $tType,X31: A,X32: proces554692349s_term @ A @ Pvar,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
% 0.16/0.39 ( ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 )
% 0.16/0.39 != ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) ) ).
% 0.16/0.39
% 0.16/0.39 % process_term.distinct(11)
% 0.16/0.39 thf(fact_37_process__term_Odistinct_I5_J,axiom,
% 0.16/0.39 ! [Pvar: $tType,A: $tType,X1: Pvar,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
% 0.16/0.39 ( ( proces1627516585ss_VAR @ Pvar @ A @ X1 )
% 0.16/0.39 != ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) ) ).
% 0.16/0.39
% 0.16/0.39 % process_term.distinct(5)
% 0.16/0.39 thf(fact_38_process__term_Odistinct_I3_J,axiom,
% 0.16/0.39 ! [Pvar: $tType,A: $tType,X1: Pvar,X31: A,X32: proces554692349s_term @ A @ Pvar] :
% 0.16/0.39 ( ( proces1627516585ss_VAR @ Pvar @ A @ X1 )
% 0.16/0.39 != ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) ) ).
% 0.16/0.39
% 0.16/0.39 % process_term.distinct(3)
% 0.16/0.39 thf(fact_39_isACT__VAR,axiom,
% 0.16/0.39 ! [C: $tType,B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X3: A] :
% 0.16/0.39 ( ( proces1121166967uarded @ A @ B @ A @ Sys )
% 0.16/0.39 => ( ( proces687458811_isACT @ A @ B @ A @ C @ Sys @ ( proces1627516585ss_VAR @ A @ C @ X3 ) )
% 0.16/0.39 = ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ ( Sys @ X3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % isACT_VAR
% 0.16/0.39 thf(fact_40_CH2_Oinduct,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,P3: ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > $o,A0: A > ( proces554692349s_term @ B @ A ),A1: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),X4: A] : ( P3 @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 0.16/0.39 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),P4: proces634752977rocess @ B] : ( P3 @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 0.16/0.39 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] : ( P3 @ Sys2 @ ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
% 0.16/0.39 => ( ! [A3: A > ( proces554692349s_term @ B @ A ),V: B,Va: proces554692349s_term @ B @ A] : ( P3 @ A3 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
% 0.16/0.39 => ( P3 @ A0 @ A1 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % CH2.induct
% 0.16/0.39 thf(fact_41_CONT_Oinduct,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,P3: ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > $o,A0: A > ( proces554692349s_term @ B @ A ),A1: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),X4: A] : ( P3 @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 0.16/0.39 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),P4: proces634752977rocess @ B] : ( P3 @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 0.16/0.39 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),A3: B,T3: proces554692349s_term @ B @ A] : ( P3 @ Sys2 @ ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) )
% 0.16/0.39 => ( ! [A3: A > ( proces554692349s_term @ B @ A ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] : ( P3 @ A3 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 0.16/0.39 => ( P3 @ A0 @ A1 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % CONT.induct
% 0.16/0.39 thf(fact_42_PREF_Oinduct,axiom,
% 0.16/0.39 ! [C: $tType,A: $tType,B: $tType,P3: ( A > ( proces554692349s_term @ B @ C ) ) > ( proces554692349s_term @ B @ A ) > $o,A0: A > ( proces554692349s_term @ B @ C ),A1: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),X4: A] : ( P3 @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 0.16/0.39 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),P4: proces634752977rocess @ B] : ( P3 @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 0.16/0.39 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),A3: B,T3: proces554692349s_term @ B @ A] : ( P3 @ Sys2 @ ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) )
% 0.16/0.39 => ( ! [A3: A > ( proces554692349s_term @ B @ C ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] : ( P3 @ A3 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 0.16/0.39 => ( P3 @ A0 @ A1 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % PREF.induct
% 0.16/0.39 thf(fact_43_guarded__def,axiom,
% 0.16/0.39 ! [C: $tType,B: $tType,A: $tType] :
% 0.16/0.39 ( ( proces1121166967uarded @ A @ B @ C )
% 0.16/0.39 = ( ^ [Sys3: A > ( proces554692349s_term @ B @ C )] :
% 0.16/0.39 ! [X5: A,Y: C] :
% 0.16/0.39 ( ( Sys3 @ X5 )
% 0.16/0.39 != ( proces1627516585ss_VAR @ C @ B @ Y ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % guarded_def
% 0.16/0.39 thf(fact_44_isACT_Oinduct,axiom,
% 0.16/0.39 ! [B: $tType,C: $tType,A: $tType,D: $tType,P3: ( A > ( proces554692349s_term @ B @ C ) ) > ( proces554692349s_term @ D @ A ) > $o,A0: A > ( proces554692349s_term @ B @ C ),A1: proces554692349s_term @ D @ A] :
% 0.16/0.39 ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),X4: A] : ( P3 @ Sys2 @ ( proces1627516585ss_VAR @ A @ D @ X4 ) )
% 0.16/0.39 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),P4: proces634752977rocess @ D] : ( P3 @ Sys2 @ ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 0.16/0.39 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),A3: D,T3: proces554692349s_term @ D @ A] : ( P3 @ Sys2 @ ( proces1454156180ss_ACT @ D @ A @ A3 @ T3 ) )
% 0.16/0.39 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] : ( P3 @ Sys2 @ ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) )
% 0.16/0.39 => ( P3 @ A0 @ A1 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % isACT.induct
% 0.16/0.39 thf(fact_45_mem__Collect__eq,axiom,
% 0.16/0.39 ! [A: $tType,A2: A,P3: A > $o] :
% 0.16/0.39 ( ( member @ A @ A2 @ ( collect @ A @ P3 ) )
% 0.16/0.39 = ( P3 @ A2 ) ) ).
% 0.16/0.39
% 0.16/0.39 % mem_Collect_eq
% 0.16/0.39 thf(fact_46_Collect__mem__eq,axiom,
% 0.16/0.39 ! [A: $tType,A4: set @ A] :
% 0.16/0.39 ( ( collect @ A
% 0.16/0.39 @ ^ [X: A] : ( member @ A @ X @ A4 ) )
% 0.16/0.39 = A4 ) ).
% 0.16/0.39
% 0.16/0.39 % Collect_mem_eq
% 0.16/0.39 thf(fact_47_Collect__cong,axiom,
% 0.16/0.39 ! [A: $tType,P3: A > $o,Q: A > $o] :
% 0.16/0.39 ( ! [X6: A] :
% 0.16/0.39 ( ( P3 @ X6 )
% 0.16/0.39 = ( Q @ X6 ) )
% 0.16/0.39 => ( ( collect @ A @ P3 )
% 0.16/0.39 = ( collect @ A @ Q ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % Collect_cong
% 0.16/0.39 thf(fact_48_ext,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.16/0.39 ( ! [X6: A] :
% 0.16/0.39 ( ( F @ X6 )
% 0.16/0.39 = ( G @ X6 ) )
% 0.16/0.39 => ( F = G ) ) ).
% 0.16/0.39
% 0.16/0.39 % ext
% 0.16/0.39 thf(fact_49_process__term_Oinduct,axiom,
% 0.16/0.39 ! [Pvar: $tType,A: $tType,P3: ( proces554692349s_term @ A @ Pvar ) > $o,Process_term: proces554692349s_term @ A @ Pvar] :
% 0.16/0.39 ( ! [X6: Pvar] : ( P3 @ ( proces1627516585ss_VAR @ Pvar @ A @ X6 ) )
% 0.16/0.39 => ( ! [X6: proces634752977rocess @ A] : ( P3 @ ( proces1062592052s_PROC @ A @ Pvar @ X6 ) )
% 0.16/0.39 => ( ! [X1a: A,X2a: proces554692349s_term @ A @ Pvar] :
% 0.16/0.39 ( ( P3 @ X2a )
% 0.16/0.39 => ( P3 @ ( proces1454156180ss_ACT @ A @ Pvar @ X1a @ X2a ) ) )
% 0.16/0.39 => ( ! [X1a: proces554692349s_term @ A @ Pvar,X2a: proces554692349s_term @ A @ Pvar] :
% 0.16/0.39 ( ( P3 @ X1a )
% 0.16/0.39 => ( ( P3 @ X2a )
% 0.16/0.39 => ( P3 @ ( proces89589571ess_CH @ A @ Pvar @ X1a @ X2a ) ) ) )
% 0.16/0.39 => ( P3 @ Process_term ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % process_term.induct
% 0.16/0.39 thf(fact_50_process__term_Oexhaust,axiom,
% 0.16/0.39 ! [Pvar: $tType,A: $tType,Y3: proces554692349s_term @ A @ Pvar] :
% 0.16/0.39 ( ! [X13: Pvar] :
% 0.16/0.39 ( Y3
% 0.16/0.39 != ( proces1627516585ss_VAR @ Pvar @ A @ X13 ) )
% 0.16/0.39 => ( ! [X23: proces634752977rocess @ A] :
% 0.16/0.39 ( Y3
% 0.16/0.39 != ( proces1062592052s_PROC @ A @ Pvar @ X23 ) )
% 0.16/0.39 => ( ! [X312: A,X322: proces554692349s_term @ A @ Pvar] :
% 0.16/0.39 ( Y3
% 0.16/0.39 != ( proces1454156180ss_ACT @ A @ Pvar @ X312 @ X322 ) )
% 0.16/0.39 => ~ ! [X412: proces554692349s_term @ A @ Pvar,X422: proces554692349s_term @ A @ Pvar] :
% 0.16/0.39 ( Y3
% 0.16/0.39 != ( proces89589571ess_CH @ A @ Pvar @ X412 @ X422 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % process_term.exhaust
% 0.16/0.39 thf(fact_51_solution_Osimps_I3_J,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 0.16/0.39 => ( ( proces745025900prefOf @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 0.16/0.39 = ( proces1708129104e_PREF @ A @ B @ A @ Sys @ T2 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % solution.simps(3)
% 0.16/0.39 thf(fact_52_process__term_Opred__True,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType] :
% 0.16/0.39 ( ( proces2118920028s_term @ A @ B
% 0.16/0.39 @ ^ [Uu: A] : $true
% 0.16/0.39 @ ^ [Uu: B] : $true )
% 0.16/0.39 = ( ^ [Uu: proces554692349s_term @ A @ B] : $true ) ) ).
% 0.16/0.39
% 0.16/0.39 % process_term.pred_True
% 0.16/0.39 thf(fact_53_process_Opred__True,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( proces1205983068rocess @ A
% 0.16/0.39 @ ^ [Uu: A] : $true )
% 0.16/0.39 = ( ^ [Uu: proces634752977rocess @ A] : $true ) ) ).
% 0.16/0.39
% 0.16/0.39 % process.pred_True
% 0.16/0.39 thf(fact_54_PREF_Oelims,axiom,
% 0.16/0.39 ! [A: $tType,C: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ B @ A,Y3: B] :
% 0.16/0.39 ( ( ( proces1708129104e_PREF @ A @ B @ C @ X7 @ Xa )
% 0.16/0.39 = Y3 )
% 0.16/0.39 => ( ! [X4: A] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 0.16/0.39 => ( Y3
% 0.16/0.39 != ( proces460752237s_term @ C @ B @ B
% 0.16/0.39 @ ^ [Aa3: C] : ( undefined @ B )
% 0.16/0.39 @ ( proces745025900prefOf @ B )
% 0.16/0.39 @ ^ [A5: B,T4: proces554692349s_term @ B @ C] : A5
% 0.16/0.39 @ ^ [Aa3: proces554692349s_term @ B @ C,Ab: proces554692349s_term @ B @ C] : ( undefined @ B )
% 0.16/0.39 @ ( X7 @ X4 ) ) ) )
% 0.16/0.39 => ( ! [P4: proces634752977rocess @ B] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 0.16/0.39 => ( Y3
% 0.16/0.39 != ( proces745025900prefOf @ B @ P4 ) ) )
% 0.16/0.39 => ( ! [A3: B] :
% 0.16/0.39 ( ? [T3: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( Xa
% 0.16/0.39 = ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) )
% 0.16/0.39 => ( Y3 != A3 ) )
% 0.16/0.39 => ~ ( ? [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( Xa
% 0.16/0.39 = ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 0.16/0.39 => ( Y3
% 0.16/0.39 != ( undefined @ B ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % PREF.elims
% 0.16/0.39 thf(fact_55_isACT_Oelims_I1_J,axiom,
% 0.16/0.39 ! [D: $tType,A: $tType,B: $tType,C: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A,Y3: $o] :
% 0.16/0.39 ( ( ( proces687458811_isACT @ A @ B @ C @ D @ X7 @ Xa )
% 0.16/0.39 = Y3 )
% 0.16/0.39 => ( ! [X4: A] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces1627516585ss_VAR @ A @ D @ X4 ) )
% 0.16/0.39 => ( Y3
% 0.16/0.39 = ( ~ ( proces460752237s_term @ C @ $o @ B
% 0.16/0.39 @ ^ [Pvar2: C] : $false
% 0.16/0.39 @ ( proces10484146Action @ B )
% 0.16/0.39 @ ^ [A5: B,T4: proces554692349s_term @ B @ C] : $true
% 0.16/0.39 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 0.16/0.39 @ ( X7 @ X4 ) ) ) ) )
% 0.16/0.39 => ( ! [P4: proces634752977rocess @ D] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 0.16/0.39 => ( Y3
% 0.16/0.39 = ( ~ ( proces10484146Action @ D @ P4 ) ) ) )
% 0.16/0.39 => ( ( ? [A3: D,T3: proces554692349s_term @ D @ A] :
% 0.16/0.39 ( Xa
% 0.16/0.39 = ( proces1454156180ss_ACT @ D @ A @ A3 @ T3 ) )
% 0.16/0.39 => ~ Y3 )
% 0.16/0.39 => ~ ( ? [T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
% 0.16/0.39 ( Xa
% 0.16/0.39 = ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) )
% 0.16/0.39 => Y3 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % isACT.elims(1)
% 0.16/0.39 thf(fact_56_PREF_Osimps_I1_J,axiom,
% 0.16/0.39 ! [B: $tType,C: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ C ),X3: A] :
% 0.16/0.39 ( ( proces1708129104e_PREF @ A @ B @ C @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X3 ) )
% 0.16/0.39 = ( proces460752237s_term @ C @ B @ B
% 0.16/0.39 @ ^ [Aa3: C] : ( undefined @ B )
% 0.16/0.39 @ ( proces745025900prefOf @ B )
% 0.16/0.39 @ ^ [A5: B,T4: proces554692349s_term @ B @ C] : A5
% 0.16/0.39 @ ^ [Aa3: proces554692349s_term @ B @ C,Ab: proces554692349s_term @ B @ C] : ( undefined @ B )
% 0.16/0.39 @ ( Sys @ X3 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % PREF.simps(1)
% 0.16/0.39 thf(fact_57_isACT_Oelims_I2_J,axiom,
% 0.16/0.39 ! [C: $tType,B: $tType,A: $tType,D: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A] :
% 0.16/0.39 ( ( proces687458811_isACT @ A @ B @ C @ D @ X7 @ Xa )
% 0.16/0.39 => ( ! [X4: A] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces1627516585ss_VAR @ A @ D @ X4 ) )
% 0.16/0.39 => ~ ( proces460752237s_term @ C @ $o @ B
% 0.16/0.39 @ ^ [Pvar2: C] : $false
% 0.16/0.39 @ ( proces10484146Action @ B )
% 0.16/0.39 @ ^ [A5: B,T4: proces554692349s_term @ B @ C] : $true
% 0.16/0.39 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 0.16/0.39 @ ( X7 @ X4 ) ) )
% 0.16/0.39 => ( ! [P4: proces634752977rocess @ D] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 0.16/0.39 => ~ ( proces10484146Action @ D @ P4 ) )
% 0.16/0.39 => ~ ! [A3: D,T3: proces554692349s_term @ D @ A] :
% 0.16/0.39 ( Xa
% 0.16/0.39 != ( proces1454156180ss_ACT @ D @ A @ A3 @ T3 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % isACT.elims(2)
% 0.16/0.39 thf(fact_58_isACT_Oelims_I3_J,axiom,
% 0.16/0.39 ! [C: $tType,B: $tType,A: $tType,D: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A] :
% 0.16/0.39 ( ~ ( proces687458811_isACT @ A @ B @ C @ D @ X7 @ Xa )
% 0.16/0.39 => ( ! [X4: A] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces1627516585ss_VAR @ A @ D @ X4 ) )
% 0.16/0.39 => ( proces460752237s_term @ C @ $o @ B
% 0.16/0.39 @ ^ [Pvar2: C] : $false
% 0.16/0.39 @ ( proces10484146Action @ B )
% 0.16/0.39 @ ^ [A5: B,T4: proces554692349s_term @ B @ C] : $true
% 0.16/0.39 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 0.16/0.39 @ ( X7 @ X4 ) ) )
% 0.16/0.39 => ( ! [P4: proces634752977rocess @ D] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 0.16/0.39 => ( proces10484146Action @ D @ P4 ) )
% 0.16/0.39 => ~ ! [T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
% 0.16/0.39 ( Xa
% 0.16/0.39 != ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % isACT.elims(3)
% 0.16/0.39 thf(fact_59_solution_Osimps_I4_J,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 0.16/0.39 => ( ( proces1778668539contOf @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 0.16/0.39 = ( proces1652378886lution @ A @ B @ Sys @ ( proces126235999e_CONT @ A @ B @ Sys @ T2 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % solution.simps(4)
% 0.16/0.39 thf(fact_60_CH2_Ocases,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,X7: product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A )] :
% 0.16/0.39 ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),X4: A] :
% 0.16/0.39 ( X7
% 0.16/0.39 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) ) )
% 0.16/0.39 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),P4: proces634752977rocess @ B] :
% 0.16/0.39 ( X7
% 0.16/0.39 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) )
% 0.16/0.39 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( X7
% 0.16/0.39 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) ) )
% 0.16/0.39 => ~ ! [A3: A > ( proces554692349s_term @ B @ A ),V: B,Va: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( X7
% 0.16/0.39 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ A3 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % CH2.cases
% 0.16/0.39 thf(fact_61_CONT_Ocases,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,X7: product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A )] :
% 0.16/0.39 ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),X4: A] :
% 0.16/0.39 ( X7
% 0.16/0.39 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) ) )
% 0.16/0.39 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),P4: proces634752977rocess @ B] :
% 0.16/0.39 ( X7
% 0.16/0.39 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) )
% 0.16/0.39 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),A3: B,T3: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( X7
% 0.16/0.39 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) ) )
% 0.16/0.39 => ~ ! [A3: A > ( proces554692349s_term @ B @ A ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( X7
% 0.16/0.39 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ A3 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % CONT.cases
% 0.16/0.39 thf(fact_62_PREF_Ocases,axiom,
% 0.16/0.39 ! [C: $tType,A: $tType,B: $tType,X7: product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A )] :
% 0.16/0.39 ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),X4: A] :
% 0.16/0.39 ( X7
% 0.16/0.39 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) ) )
% 0.16/0.39 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),P4: proces634752977rocess @ B] :
% 0.16/0.39 ( X7
% 0.16/0.39 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) )
% 0.16/0.39 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),A3: B,T3: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( X7
% 0.16/0.39 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) ) )
% 0.16/0.39 => ~ ! [A3: A > ( proces554692349s_term @ B @ C ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( X7
% 0.16/0.39 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ A3 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % PREF.cases
% 0.16/0.39 thf(fact_63_isACT_Ocases,axiom,
% 0.16/0.39 ! [B: $tType,C: $tType,A: $tType,D: $tType,X7: product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A )] :
% 0.16/0.39 ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),X4: A] :
% 0.16/0.39 ( X7
% 0.16/0.39 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys2 @ ( proces1627516585ss_VAR @ A @ D @ X4 ) ) )
% 0.16/0.39 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),P4: proces634752977rocess @ D] :
% 0.16/0.39 ( X7
% 0.16/0.39 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys2 @ ( proces1062592052s_PROC @ D @ A @ P4 ) ) )
% 0.16/0.39 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),A3: D,T3: proces554692349s_term @ D @ A] :
% 0.16/0.39 ( X7
% 0.16/0.39 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys2 @ ( proces1454156180ss_ACT @ D @ A @ A3 @ T3 ) ) )
% 0.16/0.39 => ~ ! [Sys2: A > ( proces554692349s_term @ B @ C ),T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
% 0.16/0.39 ( X7
% 0.16/0.39 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys2 @ ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % isACT.cases
% 0.16/0.39 thf(fact_64_solution_Odisc__iff_I1_J,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( ( proces10484146Action @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 0.16/0.39 = ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 ) ) ).
% 0.16/0.39
% 0.16/0.39 % solution.disc_iff(1)
% 0.16/0.39 thf(fact_65_process_Ocollapse_I1_J,axiom,
% 0.16/0.39 ! [A: $tType,Process: proces634752977rocess @ A] :
% 0.16/0.39 ( ( proces10484146Action @ A @ Process )
% 0.16/0.39 => ( ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) )
% 0.16/0.39 = Process ) ) ).
% 0.16/0.39
% 0.16/0.39 % process.collapse(1)
% 0.16/0.39 thf(fact_66_contOf__def,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( proces1778668539contOf @ A )
% 0.16/0.39 = ( proces1406508781rocess @ A @ ( proces634752977rocess @ A )
% 0.16/0.39 @ ^ [X112: A,X123: proces634752977rocess @ A] : X123
% 0.16/0.39 @ ^ [Uu2: proces634752977rocess @ A,Uv: proces634752977rocess @ A] : ( undefined @ ( proces634752977rocess @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % contOf_def
% 0.16/0.39 thf(fact_67_process_Odisc__eq__case_I1_J,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( proces10484146Action @ A )
% 0.16/0.39 = ( proces1406508781rocess @ A @ $o
% 0.16/0.39 @ ^ [Uu: A,Uv2: proces634752977rocess @ A] : $true
% 0.16/0.39 @ ^ [Uu: proces634752977rocess @ A,Uv2: proces634752977rocess @ A] : $false ) ) ).
% 0.16/0.39
% 0.16/0.39 % process.disc_eq_case(1)
% 0.16/0.39 thf(fact_68_isAction__def,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( proces10484146Action @ A )
% 0.16/0.39 = ( ^ [Process2: proces634752977rocess @ A] :
% 0.16/0.39 ? [X112: A,X123: proces634752977rocess @ A] :
% 0.16/0.39 ( Process2
% 0.16/0.39 = ( proces1525233512Action @ A @ X112 @ X123 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % isAction_def
% 0.16/0.39 thf(fact_69_process_OdiscI_I1_J,axiom,
% 0.16/0.39 ! [A: $tType,Process: proces634752977rocess @ A,X11: A,X122: proces634752977rocess @ A] :
% 0.16/0.39 ( ( Process
% 0.16/0.39 = ( proces1525233512Action @ A @ X11 @ X122 ) )
% 0.16/0.39 => ( proces10484146Action @ A @ Process ) ) ).
% 0.16/0.39
% 0.16/0.39 % process.discI(1)
% 0.16/0.39 thf(fact_70_process_Odisc_I1_J,axiom,
% 0.16/0.39 ! [A: $tType,X11: A,X122: proces634752977rocess @ A] : ( proces10484146Action @ A @ ( proces1525233512Action @ A @ X11 @ X122 ) ) ).
% 0.16/0.39
% 0.16/0.39 % process.disc(1)
% 0.16/0.39 thf(fact_71_process_Osel_I2_J,axiom,
% 0.16/0.39 ! [A: $tType,X11: A,X122: proces634752977rocess @ A] :
% 0.16/0.39 ( ( proces1778668539contOf @ A @ ( proces1525233512Action @ A @ X11 @ X122 ) )
% 0.16/0.39 = X122 ) ).
% 0.16/0.39
% 0.16/0.39 % process.sel(2)
% 0.16/0.39 thf(fact_72_CONT_Osimps_I1_J,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X3: A] :
% 0.16/0.39 ( ( proces126235999e_CONT @ A @ B @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X3 ) )
% 0.16/0.39 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 0.16/0.39 @ ^ [Aa3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.16/0.39 @ ^ [P5: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P5 ) )
% 0.16/0.39 @ ^ [A5: B,T4: proces554692349s_term @ B @ A] : T4
% 0.16/0.39 @ ^ [Aa3: proces554692349s_term @ B @ A,Ab: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.16/0.39 @ ( Sys @ X3 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % CONT.simps(1)
% 0.16/0.39 thf(fact_73_isACT_Osimps_I2_J,axiom,
% 0.16/0.39 ! [A: $tType,C: $tType,B: $tType,D: $tType,Sys: A > ( proces554692349s_term @ B @ C ),P: proces634752977rocess @ D] :
% 0.16/0.39 ( ( proces687458811_isACT @ A @ B @ C @ D @ Sys @ ( proces1062592052s_PROC @ D @ A @ P ) )
% 0.16/0.39 = ( proces10484146Action @ D @ P ) ) ).
% 0.16/0.39
% 0.16/0.39 % isACT.simps(2)
% 0.16/0.39 thf(fact_74_solution_Odisc_I1_J,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 0.16/0.39 => ( proces10484146Action @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % solution.disc(1)
% 0.16/0.39 thf(fact_75_isACT_Osimps_I1_J,axiom,
% 0.16/0.39 ! [D: $tType,B: $tType,C: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ C ),X3: A] :
% 0.16/0.39 ( ( proces687458811_isACT @ A @ B @ C @ D @ Sys @ ( proces1627516585ss_VAR @ A @ D @ X3 ) )
% 0.16/0.39 = ( proces460752237s_term @ C @ $o @ B
% 0.16/0.39 @ ^ [Pvar2: C] : $false
% 0.16/0.39 @ ( proces10484146Action @ B )
% 0.16/0.39 @ ^ [A5: B,T4: proces554692349s_term @ B @ C] : $true
% 0.16/0.39 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 0.16/0.39 @ ( Sys @ X3 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % isACT.simps(1)
% 0.16/0.39 thf(fact_76_CONT_Osimps_I2_J,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),P: proces634752977rocess @ B] :
% 0.16/0.39 ( ( proces126235999e_CONT @ A @ B @ Sys @ ( proces1062592052s_PROC @ B @ A @ P ) )
% 0.16/0.39 = ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % CONT.simps(2)
% 0.16/0.39 thf(fact_77_prefOf__def,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( proces745025900prefOf @ A )
% 0.16/0.39 = ( proces1406508781rocess @ A @ A
% 0.16/0.39 @ ^ [X112: A,X123: proces634752977rocess @ A] : X112
% 0.16/0.39 @ ^ [Uu2: proces634752977rocess @ A,Uv: proces634752977rocess @ A] : ( undefined @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % prefOf_def
% 0.16/0.39 thf(fact_78_CONT_Oelims,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y3: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( ( ( proces126235999e_CONT @ A @ B @ X7 @ Xa )
% 0.16/0.39 = Y3 )
% 0.16/0.39 => ( ! [X4: A] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 0.16/0.39 => ( Y3
% 0.16/0.39 != ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 0.16/0.39 @ ^ [Aa3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.16/0.39 @ ^ [P5: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P5 ) )
% 0.16/0.39 @ ^ [A5: B,T4: proces554692349s_term @ B @ A] : T4
% 0.16/0.39 @ ^ [Aa3: proces554692349s_term @ B @ A,Ab: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.16/0.39 @ ( X7 @ X4 ) ) ) )
% 0.16/0.39 => ( ! [P4: proces634752977rocess @ B] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 0.16/0.39 => ( Y3
% 0.16/0.39 != ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P4 ) ) ) )
% 0.16/0.39 => ( ! [A3: B,T3: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) )
% 0.16/0.39 => ( Y3 != T3 ) )
% 0.16/0.39 => ~ ( ? [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( Xa
% 0.16/0.39 = ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 0.16/0.39 => ( Y3
% 0.16/0.39 != ( undefined @ ( proces554692349s_term @ B @ A ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % CONT.elims
% 0.16/0.39 thf(fact_79_old_Oprod_Oinject,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,A2: A,B2: B,A6: A,B3: B] :
% 0.16/0.39 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.16/0.39 = ( product_Pair @ A @ B @ A6 @ B3 ) )
% 0.16/0.39 = ( ( A2 = A6 )
% 0.16/0.39 & ( B2 = B3 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % old.prod.inject
% 0.16/0.39 thf(fact_80_prod_Oinject,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,X1: A,X2: B,Y1: A,Y2: B] :
% 0.16/0.39 ( ( ( product_Pair @ A @ B @ X1 @ X2 )
% 0.16/0.39 = ( product_Pair @ A @ B @ Y1 @ Y2 ) )
% 0.16/0.39 = ( ( X1 = Y1 )
% 0.16/0.39 & ( X2 = Y2 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % prod.inject
% 0.16/0.39 thf(fact_81_PREF_Opelims,axiom,
% 0.16/0.39 ! [C: $tType,A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ B @ A,Y3: B] :
% 0.16/0.39 ( ( ( proces1708129104e_PREF @ A @ B @ C @ X7 @ Xa )
% 0.16/0.39 = Y3 )
% 0.16/0.39 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces527360425EF_rel @ A @ B @ C ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ Xa ) )
% 0.16/0.39 => ( ! [X4: A] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 0.16/0.39 => ( ( Y3
% 0.16/0.39 = ( proces460752237s_term @ C @ B @ B
% 0.16/0.39 @ ^ [Aa3: C] : ( undefined @ B )
% 0.16/0.39 @ ( proces745025900prefOf @ B )
% 0.16/0.39 @ ^ [A5: B,T4: proces554692349s_term @ B @ C] : A5
% 0.16/0.39 @ ^ [Aa3: proces554692349s_term @ B @ C,Ab: proces554692349s_term @ B @ C] : ( undefined @ B )
% 0.16/0.39 @ ( X7 @ X4 ) ) )
% 0.16/0.39 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces527360425EF_rel @ A @ B @ C ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) ) ) ) )
% 0.16/0.39 => ( ! [P4: proces634752977rocess @ B] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 0.16/0.39 => ( ( Y3
% 0.16/0.39 = ( proces745025900prefOf @ B @ P4 ) )
% 0.16/0.39 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces527360425EF_rel @ A @ B @ C ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) ) ) )
% 0.16/0.39 => ( ! [A3: B,T3: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) )
% 0.16/0.39 => ( ( Y3 = A3 )
% 0.16/0.39 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces527360425EF_rel @ A @ B @ C ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) ) ) ) )
% 0.16/0.39 => ~ ! [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 0.16/0.39 => ( ( Y3
% 0.16/0.39 = ( undefined @ B ) )
% 0.16/0.39 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces527360425EF_rel @ A @ B @ C ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % PREF.pelims
% 0.16/0.39 thf(fact_82_CONT_Opelims,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y3: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( ( ( proces126235999e_CONT @ A @ B @ X7 @ Xa )
% 0.16/0.39 = Y3 )
% 0.16/0.39 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1004198490NT_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ Xa ) )
% 0.16/0.39 => ( ! [X4: A] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 0.16/0.39 => ( ( Y3
% 0.16/0.39 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 0.16/0.39 @ ^ [Aa3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.16/0.39 @ ^ [P5: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P5 ) )
% 0.16/0.39 @ ^ [A5: B,T4: proces554692349s_term @ B @ A] : T4
% 0.16/0.39 @ ^ [Aa3: proces554692349s_term @ B @ A,Ab: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.16/0.39 @ ( X7 @ X4 ) ) )
% 0.16/0.39 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1004198490NT_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) ) ) ) )
% 0.16/0.39 => ( ! [P4: proces634752977rocess @ B] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 0.16/0.39 => ( ( Y3
% 0.16/0.39 = ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P4 ) ) )
% 0.16/0.39 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1004198490NT_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) ) ) )
% 0.16/0.39 => ( ! [A3: B,T3: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) )
% 0.16/0.39 => ( ( Y3 = T3 )
% 0.16/0.39 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1004198490NT_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) ) ) ) )
% 0.16/0.39 => ~ ! [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 0.16/0.39 => ( ( Y3
% 0.16/0.39 = ( undefined @ ( proces554692349s_term @ B @ A ) ) )
% 0.16/0.39 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1004198490NT_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % CONT.pelims
% 0.16/0.39 thf(fact_83_isACT_Opelims_I1_J,axiom,
% 0.16/0.39 ! [B: $tType,C: $tType,A: $tType,D: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A,Y3: $o] :
% 0.16/0.39 ( ( ( proces687458811_isACT @ A @ B @ C @ D @ X7 @ Xa )
% 0.16/0.39 = Y3 )
% 0.16/0.39 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ Xa ) )
% 0.16/0.39 => ( ! [X4: A] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces1627516585ss_VAR @ A @ D @ X4 ) )
% 0.16/0.39 => ( ( Y3
% 0.16/0.39 = ( proces460752237s_term @ C @ $o @ B
% 0.16/0.39 @ ^ [Pvar2: C] : $false
% 0.16/0.39 @ ( proces10484146Action @ B )
% 0.16/0.39 @ ^ [A5: B,T4: proces554692349s_term @ B @ C] : $true
% 0.16/0.39 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 0.16/0.39 @ ( X7 @ X4 ) ) )
% 0.16/0.39 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ ( proces1627516585ss_VAR @ A @ D @ X4 ) ) ) ) )
% 0.16/0.39 => ( ! [P4: proces634752977rocess @ D] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 0.16/0.39 => ( ( Y3
% 0.16/0.39 = ( proces10484146Action @ D @ P4 ) )
% 0.16/0.39 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ ( proces1062592052s_PROC @ D @ A @ P4 ) ) ) ) )
% 0.16/0.39 => ( ! [A3: D,T3: proces554692349s_term @ D @ A] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces1454156180ss_ACT @ D @ A @ A3 @ T3 ) )
% 0.16/0.39 => ( Y3
% 0.16/0.39 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ ( proces1454156180ss_ACT @ D @ A @ A3 @ T3 ) ) ) ) )
% 0.16/0.39 => ~ ! [T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) )
% 0.16/0.39 => ( ~ Y3
% 0.16/0.39 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % isACT.pelims(1)
% 0.16/0.39 thf(fact_84_isACT_Opelims_I2_J,axiom,
% 0.16/0.39 ! [B: $tType,C: $tType,A: $tType,D: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A] :
% 0.16/0.39 ( ( proces687458811_isACT @ A @ B @ C @ D @ X7 @ Xa )
% 0.16/0.39 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ Xa ) )
% 0.16/0.39 => ( ! [X4: A] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces1627516585ss_VAR @ A @ D @ X4 ) )
% 0.16/0.39 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ ( proces1627516585ss_VAR @ A @ D @ X4 ) ) )
% 0.16/0.39 => ~ ( proces460752237s_term @ C @ $o @ B
% 0.16/0.39 @ ^ [Pvar2: C] : $false
% 0.16/0.39 @ ( proces10484146Action @ B )
% 0.16/0.39 @ ^ [A5: B,T4: proces554692349s_term @ B @ C] : $true
% 0.16/0.39 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 0.16/0.39 @ ( X7 @ X4 ) ) ) )
% 0.16/0.39 => ( ! [P4: proces634752977rocess @ D] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 0.16/0.39 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ ( proces1062592052s_PROC @ D @ A @ P4 ) ) )
% 0.16/0.39 => ~ ( proces10484146Action @ D @ P4 ) ) )
% 0.16/0.39 => ~ ! [A3: D,T3: proces554692349s_term @ D @ A] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces1454156180ss_ACT @ D @ A @ A3 @ T3 ) )
% 0.16/0.39 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ ( proces1454156180ss_ACT @ D @ A @ A3 @ T3 ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % isACT.pelims(2)
% 0.16/0.39 thf(fact_85_isACT_Opelims_I3_J,axiom,
% 0.16/0.39 ! [B: $tType,C: $tType,A: $tType,D: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A] :
% 0.16/0.39 ( ~ ( proces687458811_isACT @ A @ B @ C @ D @ X7 @ Xa )
% 0.16/0.39 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ Xa ) )
% 0.16/0.39 => ( ! [X4: A] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces1627516585ss_VAR @ A @ D @ X4 ) )
% 0.16/0.39 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ ( proces1627516585ss_VAR @ A @ D @ X4 ) ) )
% 0.16/0.39 => ( proces460752237s_term @ C @ $o @ B
% 0.16/0.39 @ ^ [Pvar2: C] : $false
% 0.16/0.39 @ ( proces10484146Action @ B )
% 0.16/0.39 @ ^ [A5: B,T4: proces554692349s_term @ B @ C] : $true
% 0.16/0.39 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 0.16/0.39 @ ( X7 @ X4 ) ) ) )
% 0.16/0.39 => ( ! [P4: proces634752977rocess @ D] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 0.16/0.39 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ ( proces1062592052s_PROC @ D @ A @ P4 ) ) )
% 0.16/0.39 => ( proces10484146Action @ D @ P4 ) ) )
% 0.16/0.39 => ~ ! [T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) )
% 0.16/0.39 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % isACT.pelims(3)
% 0.16/0.39 thf(fact_86_surj__pair,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,P: product_prod @ A @ B] :
% 0.16/0.39 ? [X6: A,Y4: B] :
% 0.16/0.39 ( P
% 0.16/0.39 = ( product_Pair @ A @ B @ X6 @ Y4 ) ) ).
% 0.16/0.39
% 0.16/0.39 % surj_pair
% 0.16/0.39 thf(fact_87_prod__cases,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType,P3: ( product_prod @ A @ B ) > $o,P: product_prod @ A @ B] :
% 0.16/0.39 ( ! [A3: A,B4: B] : ( P3 @ ( product_Pair @ A @ B @ A3 @ B4 ) )
% 0.16/0.39 => ( P3 @ P ) ) ).
% 0.16/0.39
% 0.16/0.39 % prod_cases
% 0.16/0.39 thf(fact_88_Pair__inject,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,A2: A,B2: B,A6: A,B3: B] :
% 0.16/0.39 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.16/0.39 = ( product_Pair @ A @ B @ A6 @ B3 ) )
% 0.16/0.39 => ~ ( ( A2 = A6 )
% 0.16/0.39 => ( B2 != B3 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % Pair_inject
% 0.16/0.39 thf(fact_89_prod__cases3,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,C: $tType,Y3: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.16/0.39 ~ ! [A3: A,B4: B,C2: C] :
% 0.16/0.39 ( Y3
% 0.16/0.39 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A3 @ ( product_Pair @ B @ C @ B4 @ C2 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % prod_cases3
% 0.16/0.39 thf(fact_90_prod__cases4,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.16/0.39 ~ ! [A3: A,B4: B,C2: C,D2: D] :
% 0.16/0.39 ( Y3
% 0.16/0.39 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % prod_cases4
% 0.16/0.39 thf(fact_91_prod__cases5,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,Y3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 0.16/0.39 ~ ! [A3: A,B4: B,C2: C,D2: D,E2: E] :
% 0.16/0.39 ( Y3
% 0.16/0.39 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C2 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % prod_cases5
% 0.16/0.39 thf(fact_92_prod__cases6,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F5: $tType,Y3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) )] :
% 0.16/0.39 ~ ! [A3: A,B4: B,C2: C,D2: D,E2: E,F6: F5] :
% 0.16/0.39 ( Y3
% 0.16/0.39 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ F5 ) @ D2 @ ( product_Pair @ E @ F5 @ E2 @ F6 ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % prod_cases6
% 0.16/0.39 thf(fact_93_prod__cases7,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F5: $tType,G2: $tType,Y3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) ) )] :
% 0.16/0.39 ~ ! [A3: A,B4: B,C2: C,D2: D,E2: E,F6: F5,G3: G2] :
% 0.16/0.39 ( Y3
% 0.16/0.39 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F5 @ G2 ) @ E2 @ ( product_Pair @ F5 @ G2 @ F6 @ G3 ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % prod_cases7
% 0.16/0.39 thf(fact_94_prod__induct3,axiom,
% 0.16/0.39 ! [C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X7: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.16/0.39 ( ! [A3: A,B4: B,C2: C] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A3 @ ( product_Pair @ B @ C @ B4 @ C2 ) ) )
% 0.16/0.39 => ( P3 @ X7 ) ) ).
% 0.16/0.39
% 0.16/0.39 % prod_induct3
% 0.16/0.39 thf(fact_95_prod__induct4,axiom,
% 0.16/0.39 ! [D: $tType,C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X7: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.16/0.39 ( ! [A3: A,B4: B,C2: C,D2: D] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) )
% 0.16/0.39 => ( P3 @ X7 ) ) ).
% 0.16/0.39
% 0.16/0.39 % prod_induct4
% 0.16/0.39 thf(fact_96_prod__induct5,axiom,
% 0.16/0.39 ! [E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) > $o,X7: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 0.16/0.39 ( ! [A3: A,B4: B,C2: C,D2: D,E2: E] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C2 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) )
% 0.16/0.39 => ( P3 @ X7 ) ) ).
% 0.16/0.39
% 0.16/0.39 % prod_induct5
% 0.16/0.39 thf(fact_97_prod__induct6,axiom,
% 0.16/0.39 ! [F5: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) ) ) > $o,X7: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) )] :
% 0.16/0.39 ( ! [A3: A,B4: B,C2: C,D2: D,E2: E,F6: F5] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ F5 ) @ D2 @ ( product_Pair @ E @ F5 @ E2 @ F6 ) ) ) ) ) )
% 0.16/0.39 => ( P3 @ X7 ) ) ).
% 0.16/0.39
% 0.16/0.39 % prod_induct6
% 0.16/0.39 thf(fact_98_prod__induct7,axiom,
% 0.16/0.39 ! [G2: $tType,F5: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) ) ) ) > $o,X7: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) ) )] :
% 0.16/0.39 ( ! [A3: A,B4: B,C2: C,D2: D,E2: E,F6: F5,G3: G2] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F5 @ G2 ) @ E2 @ ( product_Pair @ F5 @ G2 @ F6 @ G3 ) ) ) ) ) ) )
% 0.16/0.39 => ( P3 @ X7 ) ) ).
% 0.16/0.39
% 0.16/0.39 % prod_induct7
% 0.16/0.39 thf(fact_99_old_Oprod_Oexhaust,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,Y3: product_prod @ A @ B] :
% 0.16/0.39 ~ ! [A3: A,B4: B] :
% 0.16/0.39 ( Y3
% 0.16/0.39 != ( product_Pair @ A @ B @ A3 @ B4 ) ) ).
% 0.16/0.39
% 0.16/0.39 % old.prod.exhaust
% 0.16/0.39 thf(fact_100_old_Oprod_Oinducts,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType,P3: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 0.16/0.39 ( ! [A3: A,B4: B] : ( P3 @ ( product_Pair @ A @ B @ A3 @ B4 ) )
% 0.16/0.39 => ( P3 @ Prod ) ) ).
% 0.16/0.39
% 0.16/0.39 % old.prod.inducts
% 0.16/0.39 thf(fact_101_old_Oprod_Orec,axiom,
% 0.16/0.39 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 0.16/0.39 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.16/0.39 = ( F1 @ A2 @ B2 ) ) ).
% 0.16/0.39
% 0.16/0.39 % old.prod.rec
% 0.16/0.39 thf(fact_102_CH1_Oelims,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y3: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( ( ( proces1239275103le_CH1 @ A @ B @ X7 @ Xa )
% 0.16/0.39 = Y3 )
% 0.16/0.39 => ( ! [X4: A] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 0.16/0.39 => ( Y3
% 0.16/0.39 != ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 0.16/0.39 @ ^ [A5: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.16/0.39 @ ^ [P5: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P5 ) )
% 0.16/0.39 @ ^ [A5: B,B5: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.16/0.39 @ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T13
% 0.16/0.39 @ ( X7 @ X4 ) ) ) )
% 0.16/0.39 => ( ! [P4: proces634752977rocess @ B] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 0.16/0.39 => ( Y3
% 0.16/0.39 != ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P4 ) ) ) )
% 0.16/0.39 => ( ! [T12: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( ? [T23: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( Xa
% 0.16/0.39 = ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
% 0.16/0.39 => ( Y3 != T12 ) )
% 0.16/0.39 => ~ ( ? [V: B,Va: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( Xa
% 0.16/0.39 = ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
% 0.16/0.39 => ( Y3
% 0.16/0.39 != ( undefined @ ( proces554692349s_term @ B @ A ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % CH1.elims
% 0.16/0.39 thf(fact_103_CH2_Oelims,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y3: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( ( ( proces1239275104le_CH2 @ A @ B @ X7 @ Xa )
% 0.16/0.39 = Y3 )
% 0.16/0.39 => ( ! [X4: A] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 0.16/0.39 => ( Y3
% 0.16/0.39 != ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 0.16/0.39 @ ^ [A5: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.16/0.39 @ ^ [P5: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P5 ) )
% 0.16/0.39 @ ^ [A5: B,B5: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.16/0.39 @ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T24
% 0.16/0.39 @ ( X7 @ X4 ) ) ) )
% 0.16/0.39 => ( ! [P4: proces634752977rocess @ B] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 0.16/0.39 => ( Y3
% 0.16/0.39 != ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P4 ) ) ) )
% 0.16/0.39 => ( ! [T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
% 0.16/0.39 => ( Y3 != T23 ) )
% 0.16/0.39 => ~ ( ? [V: B,Va: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( Xa
% 0.16/0.39 = ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
% 0.16/0.39 => ( Y3
% 0.16/0.39 != ( undefined @ ( proces554692349s_term @ B @ A ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % CH2.elims
% 0.16/0.39 thf(fact_104_CH1_Opelims,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y3: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( ( ( proces1239275103le_CH1 @ A @ B @ X7 @ Xa )
% 0.16/0.39 = Y3 )
% 0.16/0.39 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1869379930H1_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ Xa ) )
% 0.16/0.39 => ( ! [X4: A] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 0.16/0.39 => ( ( Y3
% 0.16/0.39 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 0.16/0.39 @ ^ [A5: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.16/0.39 @ ^ [P5: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P5 ) )
% 0.16/0.39 @ ^ [A5: B,B5: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.16/0.39 @ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T13
% 0.16/0.39 @ ( X7 @ X4 ) ) )
% 0.16/0.39 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1869379930H1_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) ) ) ) )
% 0.16/0.39 => ( ! [P4: proces634752977rocess @ B] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 0.16/0.39 => ( ( Y3
% 0.16/0.39 = ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P4 ) ) )
% 0.16/0.39 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1869379930H1_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) ) ) )
% 0.16/0.39 => ( ! [T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
% 0.16/0.39 => ( ( Y3 = T12 )
% 0.16/0.39 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1869379930H1_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) ) ) ) )
% 0.16/0.39 => ~ ! [V: B,Va: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
% 0.16/0.39 => ( ( Y3
% 0.16/0.39 = ( undefined @ ( proces554692349s_term @ B @ A ) ) )
% 0.16/0.39 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1869379930H1_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % CH1.pelims
% 0.16/0.39 thf(fact_105_CH2_Opelims,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y3: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( ( ( proces1239275104le_CH2 @ A @ B @ X7 @ Xa )
% 0.16/0.39 = Y3 )
% 0.16/0.39 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces93903513H2_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ Xa ) )
% 0.16/0.39 => ( ! [X4: A] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 0.16/0.39 => ( ( Y3
% 0.16/0.39 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 0.16/0.39 @ ^ [A5: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.16/0.39 @ ^ [P5: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P5 ) )
% 0.16/0.39 @ ^ [A5: B,B5: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.16/0.39 @ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T24
% 0.16/0.39 @ ( X7 @ X4 ) ) )
% 0.16/0.39 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces93903513H2_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) ) ) ) )
% 0.16/0.39 => ( ! [P4: proces634752977rocess @ B] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 0.16/0.39 => ( ( Y3
% 0.16/0.39 = ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P4 ) ) )
% 0.16/0.39 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces93903513H2_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) ) ) )
% 0.16/0.39 => ( ! [T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
% 0.16/0.39 => ( ( Y3 = T23 )
% 0.16/0.39 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces93903513H2_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) ) ) ) )
% 0.16/0.39 => ~ ! [V: B,Va: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
% 0.16/0.39 => ( ( Y3
% 0.16/0.39 = ( undefined @ ( proces554692349s_term @ B @ A ) ) )
% 0.16/0.39 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces93903513H2_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % CH2.pelims
% 0.16/0.39 thf(fact_106_ch1Of__def,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( proces979765041_ch1Of @ A )
% 0.16/0.39 = ( proces1406508781rocess @ A @ ( proces634752977rocess @ A )
% 0.16/0.39 @ ^ [Uu2: A,Uv: proces634752977rocess @ A] : ( undefined @ ( proces634752977rocess @ A ) )
% 0.16/0.39 @ ^ [X21: proces634752977rocess @ A,X222: proces634752977rocess @ A] : X21 ) ) ).
% 0.16/0.39
% 0.16/0.39 % ch1Of_def
% 0.16/0.39 thf(fact_107_CH2_Osimps_I2_J,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),P: proces634752977rocess @ B] :
% 0.16/0.39 ( ( proces1239275104le_CH2 @ A @ B @ Sys @ ( proces1062592052s_PROC @ B @ A @ P ) )
% 0.16/0.39 = ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % CH2.simps(2)
% 0.16/0.39 thf(fact_108_CH1_Osimps_I2_J,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),P: proces634752977rocess @ B] :
% 0.16/0.39 ( ( proces1239275103le_CH1 @ A @ B @ Sys @ ( proces1062592052s_PROC @ B @ A @ P ) )
% 0.16/0.39 = ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % CH1.simps(2)
% 0.16/0.39 thf(fact_109_solution_Osimps_I6_J,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 0.16/0.39 => ( ( proces988026546_ch2Of @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 0.16/0.39 = ( proces1652378886lution @ A @ B @ Sys @ ( proces1239275104le_CH2 @ A @ B @ Sys @ T2 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % solution.simps(6)
% 0.16/0.39 thf(fact_110_solution_Osimps_I5_J,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 0.16/0.39 => ( ( proces979765041_ch1Of @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 0.16/0.39 = ( proces1652378886lution @ A @ B @ Sys @ ( proces1239275103le_CH1 @ A @ B @ Sys @ T2 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % solution.simps(5)
% 0.16/0.39 thf(fact_111_CH2_Osimps_I3_J,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T1: proces554692349s_term @ B @ A,T22: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( ( proces1239275104le_CH2 @ A @ B @ Sys @ ( proces89589571ess_CH @ B @ A @ T1 @ T22 ) )
% 0.16/0.39 = T22 ) ).
% 0.16/0.39
% 0.16/0.39 % CH2.simps(3)
% 0.16/0.39 thf(fact_112_CH1_Osimps_I3_J,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T1: proces554692349s_term @ B @ A,T22: proces554692349s_term @ B @ A] :
% 0.16/0.39 ( ( proces1239275103le_CH1 @ A @ B @ Sys @ ( proces89589571ess_CH @ B @ A @ T1 @ T22 ) )
% 0.16/0.39 = T1 ) ).
% 0.16/0.39
% 0.16/0.39 % CH1.simps(3)
% 0.16/0.39 thf(fact_113_process_Ocase__eq__if,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType] :
% 0.16/0.39 ( ( proces1406508781rocess @ A @ B )
% 0.16/0.39 = ( ^ [F12: A > ( proces634752977rocess @ A ) > B,F22: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process2: proces634752977rocess @ A] : ( if @ B @ ( proces10484146Action @ A @ Process2 ) @ ( F12 @ ( proces745025900prefOf @ A @ Process2 ) @ ( proces1778668539contOf @ A @ Process2 ) ) @ ( F22 @ ( proces979765041_ch1Of @ A @ Process2 ) @ ( proces988026546_ch2Of @ A @ Process2 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % process.case_eq_if
% 0.16/0.39 thf(fact_114_CH2_Osimps_I1_J,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X3: A] :
% 0.16/0.39 ( ( proces1239275104le_CH2 @ A @ B @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X3 ) )
% 0.16/0.39 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 0.16/0.39 @ ^ [A5: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.16/0.39 @ ^ [P5: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P5 ) )
% 0.16/0.39 @ ^ [A5: B,B5: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.16/0.39 @ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T24
% 0.16/0.39 @ ( Sys @ X3 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % CH2.simps(1)
% 0.16/0.39 thf(fact_115_CH1_Osimps_I1_J,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X3: A] :
% 0.16/0.39 ( ( proces1239275103le_CH1 @ A @ B @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X3 ) )
% 0.16/0.39 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 0.16/0.39 @ ^ [A5: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.16/0.39 @ ^ [P5: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P5 ) )
% 0.16/0.39 @ ^ [A5: B,B5: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 0.16/0.39 @ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T13
% 0.16/0.39 @ ( Sys @ X3 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % CH1.simps(1)
% 0.16/0.39 thf(fact_116_ch2Of__def,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( proces988026546_ch2Of @ A )
% 0.16/0.39 = ( proces1406508781rocess @ A @ ( proces634752977rocess @ A )
% 0.16/0.39 @ ^ [Uu2: A,Uv: proces634752977rocess @ A] : ( undefined @ ( proces634752977rocess @ A ) )
% 0.16/0.39 @ ^ [X21: proces634752977rocess @ A,X222: proces634752977rocess @ A] : X222 ) ) ).
% 0.16/0.39
% 0.16/0.39 % ch2Of_def
% 0.16/0.39 thf(fact_117_solution_Ocode,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType] :
% 0.16/0.39 ( ( proces1652378886lution @ A @ B )
% 0.16/0.39 = ( ^ [Sys3: A > ( proces554692349s_term @ B @ A ),T4: proces554692349s_term @ B @ A] : ( if @ ( proces634752977rocess @ B ) @ ( proces687458811_isACT @ A @ B @ A @ B @ Sys3 @ T4 ) @ ( proces1525233512Action @ B @ ( proces1708129104e_PREF @ A @ B @ A @ Sys3 @ T4 ) @ ( proces1652378886lution @ A @ B @ Sys3 @ ( proces126235999e_CONT @ A @ B @ Sys3 @ T4 ) ) ) @ ( proces1915862579Choice @ B @ ( proces1652378886lution @ A @ B @ Sys3 @ ( proces1239275103le_CH1 @ A @ B @ Sys3 @ T4 ) ) @ ( proces1652378886lution @ A @ B @ Sys3 @ ( proces1239275104le_CH2 @ A @ B @ Sys3 @ T4 ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % solution.code
% 0.16/0.39 thf(fact_118_process_Osplit__sel__asm,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType,P3: B > $o,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process: proces634752977rocess @ A] :
% 0.16/0.39 ( ( P3 @ ( proces1406508781rocess @ A @ B @ F1 @ F2 @ Process ) )
% 0.16/0.39 = ( ~ ( ( ( Process
% 0.16/0.39 = ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) )
% 0.16/0.39 & ~ ( P3 @ ( F1 @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) ) )
% 0.16/0.39 | ( ( Process
% 0.16/0.39 = ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) )
% 0.16/0.39 & ~ ( P3 @ ( F2 @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % process.split_sel_asm
% 0.16/0.39 thf(fact_119_process_Osplit__sel,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType,P3: B > $o,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process: proces634752977rocess @ A] :
% 0.16/0.39 ( ( P3 @ ( proces1406508781rocess @ A @ B @ F1 @ F2 @ Process ) )
% 0.16/0.39 = ( ( ( Process
% 0.16/0.39 = ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) )
% 0.16/0.39 => ( P3 @ ( F1 @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) ) )
% 0.16/0.39 & ( ( Process
% 0.16/0.39 = ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) )
% 0.16/0.39 => ( P3 @ ( F2 @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % process.split_sel
% 0.16/0.39 thf(fact_120_process_Oexpand,axiom,
% 0.16/0.39 ! [A: $tType,Process: proces634752977rocess @ A,Process3: proces634752977rocess @ A] :
% 0.16/0.39 ( ( ( proces10484146Action @ A @ Process )
% 0.16/0.39 = ( proces10484146Action @ A @ Process3 ) )
% 0.16/0.39 => ( ( ( proces10484146Action @ A @ Process )
% 0.16/0.39 => ( ( proces10484146Action @ A @ Process3 )
% 0.16/0.39 => ( ( ( proces745025900prefOf @ A @ Process )
% 0.16/0.39 = ( proces745025900prefOf @ A @ Process3 ) )
% 0.16/0.39 & ( ( proces1778668539contOf @ A @ Process )
% 0.16/0.39 = ( proces1778668539contOf @ A @ Process3 ) ) ) ) )
% 0.16/0.39 => ( ( ( proces401113213Choice @ A @ Process )
% 0.16/0.39 => ( ( proces401113213Choice @ A @ Process3 )
% 0.16/0.39 => ( ( ( proces979765041_ch1Of @ A @ Process )
% 0.16/0.39 = ( proces979765041_ch1Of @ A @ Process3 ) )
% 0.16/0.39 & ( ( proces988026546_ch2Of @ A @ Process )
% 0.16/0.39 = ( proces988026546_ch2Of @ A @ Process3 ) ) ) ) )
% 0.16/0.39 => ( Process = Process3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % process.expand
% 0.16/0.39 thf(fact_121_process_Ocoinduct,axiom,
% 0.16/0.39 ! [A: $tType,R: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,Process: proces634752977rocess @ A,Process3: proces634752977rocess @ A] :
% 0.16/0.39 ( ( R @ Process @ Process3 )
% 0.16/0.39 => ( ! [Process4: proces634752977rocess @ A,Process5: proces634752977rocess @ A] :
% 0.16/0.39 ( ( R @ Process4 @ Process5 )
% 0.16/0.39 => ( ( ( proces10484146Action @ A @ Process4 )
% 0.16/0.39 = ( proces10484146Action @ A @ Process5 ) )
% 0.16/0.39 & ( ( proces10484146Action @ A @ Process4 )
% 0.16/0.39 => ( ( proces10484146Action @ A @ Process5 )
% 0.16/0.39 => ( ( ( proces745025900prefOf @ A @ Process4 )
% 0.16/0.39 = ( proces745025900prefOf @ A @ Process5 ) )
% 0.16/0.39 & ( R @ ( proces1778668539contOf @ A @ Process4 ) @ ( proces1778668539contOf @ A @ Process5 ) ) ) ) )
% 0.16/0.39 & ( ( proces401113213Choice @ A @ Process4 )
% 0.16/0.39 => ( ( proces401113213Choice @ A @ Process5 )
% 0.16/0.39 => ( ( R @ ( proces979765041_ch1Of @ A @ Process4 ) @ ( proces979765041_ch1Of @ A @ Process5 ) )
% 0.16/0.39 & ( R @ ( proces988026546_ch2Of @ A @ Process4 ) @ ( proces988026546_ch2Of @ A @ Process5 ) ) ) ) ) ) )
% 0.16/0.39 => ( Process = Process3 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % process.coinduct
% 0.16/0.39 thf(fact_122_process_Oinject_I2_J,axiom,
% 0.16/0.39 ! [A: $tType,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A,Y21: proces634752977rocess @ A,Y22: proces634752977rocess @ A] :
% 0.16/0.39 ( ( ( proces1915862579Choice @ A @ X212 @ X223 )
% 0.16/0.40 = ( proces1915862579Choice @ A @ Y21 @ Y22 ) )
% 0.16/0.40 = ( ( X212 = Y21 )
% 0.16/0.40 & ( X223 = Y22 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.inject(2)
% 0.16/0.40 thf(fact_123_process_Opred__inject_I2_J,axiom,
% 0.16/0.40 ! [A: $tType,P3: A > $o,A2: proces634752977rocess @ A,Aa2: proces634752977rocess @ A] :
% 0.16/0.40 ( ( proces1205983068rocess @ A @ P3 @ ( proces1915862579Choice @ A @ A2 @ Aa2 ) )
% 0.16/0.40 = ( ( proces1205983068rocess @ A @ P3 @ A2 )
% 0.16/0.40 & ( proces1205983068rocess @ A @ P3 @ Aa2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.pred_inject(2)
% 0.16/0.40 thf(fact_124_solution_Odisc__iff_I2_J,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 0.16/0.40 ( ( proces401113213Choice @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 0.16/0.40 = ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % solution.disc_iff(2)
% 0.16/0.40 thf(fact_125_process_Ocollapse_I2_J,axiom,
% 0.16/0.40 ! [A: $tType,Process: proces634752977rocess @ A] :
% 0.16/0.40 ( ( proces401113213Choice @ A @ Process )
% 0.16/0.40 => ( ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) )
% 0.16/0.40 = Process ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.collapse(2)
% 0.16/0.40 thf(fact_126_process_Odisc_I4_J,axiom,
% 0.16/0.40 ! [A: $tType,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A] : ( proces401113213Choice @ A @ ( proces1915862579Choice @ A @ X212 @ X223 ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.disc(4)
% 0.16/0.40 thf(fact_127_process_OdiscI_I2_J,axiom,
% 0.16/0.40 ! [A: $tType,Process: proces634752977rocess @ A,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A] :
% 0.16/0.40 ( ( Process
% 0.16/0.40 = ( proces1915862579Choice @ A @ X212 @ X223 ) )
% 0.16/0.40 => ( proces401113213Choice @ A @ Process ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.discI(2)
% 0.16/0.40 thf(fact_128_isChoice__def,axiom,
% 0.16/0.40 ! [A: $tType] :
% 0.16/0.40 ( ( proces401113213Choice @ A )
% 0.16/0.40 = ( ^ [Process2: proces634752977rocess @ A] :
% 0.16/0.40 ? [X21: proces634752977rocess @ A,X222: proces634752977rocess @ A] :
% 0.16/0.40 ( Process2
% 0.16/0.40 = ( proces1915862579Choice @ A @ X21 @ X222 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % isChoice_def
% 0.16/0.40 thf(fact_129_process__strong__coind,axiom,
% 0.16/0.40 ! [A: $tType,Phi: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,P: proces634752977rocess @ A,P6: proces634752977rocess @ A] :
% 0.16/0.40 ( ( Phi @ P @ P6 )
% 0.16/0.40 => ( ! [P4: proces634752977rocess @ A,P7: proces634752977rocess @ A] :
% 0.16/0.40 ( ( Phi @ P4 @ P7 )
% 0.16/0.40 => ( ( ( proces10484146Action @ A @ P4 )
% 0.16/0.40 = ( proces10484146Action @ A @ P7 ) )
% 0.16/0.40 & ( ( proces401113213Choice @ A @ P4 )
% 0.16/0.40 = ( proces401113213Choice @ A @ P7 ) ) ) )
% 0.16/0.40 => ( ! [A3: A,A7: A,P4: proces634752977rocess @ A,P7: proces634752977rocess @ A] :
% 0.16/0.40 ( ( Phi @ ( proces1525233512Action @ A @ A3 @ P4 ) @ ( proces1525233512Action @ A @ A7 @ P7 ) )
% 0.16/0.40 => ( ( A3 = A7 )
% 0.16/0.40 & ( ( Phi @ P4 @ P7 )
% 0.16/0.40 | ( P4 = P7 ) ) ) )
% 0.16/0.40 => ( ! [P4: proces634752977rocess @ A,Q2: proces634752977rocess @ A,P7: proces634752977rocess @ A,Q3: proces634752977rocess @ A] :
% 0.16/0.40 ( ( Phi @ ( proces1915862579Choice @ A @ P4 @ Q2 ) @ ( proces1915862579Choice @ A @ P7 @ Q3 ) )
% 0.16/0.40 => ( ( ( Phi @ P4 @ P7 )
% 0.16/0.40 | ( P4 = P7 ) )
% 0.16/0.40 & ( ( Phi @ Q2 @ Q3 )
% 0.16/0.40 | ( Q2 = Q3 ) ) ) )
% 0.16/0.40 => ( P = P6 ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_strong_coind
% 0.16/0.40 thf(fact_130_process__coind,axiom,
% 0.16/0.40 ! [A: $tType,Phi: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,P: proces634752977rocess @ A,P6: proces634752977rocess @ A] :
% 0.16/0.40 ( ( Phi @ P @ P6 )
% 0.16/0.40 => ( ! [P4: proces634752977rocess @ A,P7: proces634752977rocess @ A] :
% 0.16/0.40 ( ( Phi @ P4 @ P7 )
% 0.16/0.40 => ( ( ( proces10484146Action @ A @ P4 )
% 0.16/0.40 = ( proces10484146Action @ A @ P7 ) )
% 0.16/0.40 & ( ( proces401113213Choice @ A @ P4 )
% 0.16/0.40 = ( proces401113213Choice @ A @ P7 ) ) ) )
% 0.16/0.40 => ( ! [A3: A,A7: A,P4: proces634752977rocess @ A,P7: proces634752977rocess @ A] :
% 0.16/0.40 ( ( Phi @ ( proces1525233512Action @ A @ A3 @ P4 ) @ ( proces1525233512Action @ A @ A7 @ P7 ) )
% 0.16/0.40 => ( ( A3 = A7 )
% 0.16/0.40 & ( Phi @ P4 @ P7 ) ) )
% 0.16/0.40 => ( ! [P4: proces634752977rocess @ A,Q2: proces634752977rocess @ A,P7: proces634752977rocess @ A,Q3: proces634752977rocess @ A] :
% 0.16/0.40 ( ( Phi @ ( proces1915862579Choice @ A @ P4 @ Q2 ) @ ( proces1915862579Choice @ A @ P7 @ Q3 ) )
% 0.16/0.40 => ( ( Phi @ P4 @ P7 )
% 0.16/0.40 & ( Phi @ Q2 @ Q3 ) ) )
% 0.16/0.40 => ( P = P6 ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_coind
% 0.16/0.40 thf(fact_131_process_Odisc_I2_J,axiom,
% 0.16/0.40 ! [A: $tType,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A] :
% 0.16/0.40 ~ ( proces10484146Action @ A @ ( proces1915862579Choice @ A @ X212 @ X223 ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.disc(2)
% 0.16/0.40 thf(fact_132_process_Odistinct_I1_J,axiom,
% 0.16/0.40 ! [A: $tType,X11: A,X122: proces634752977rocess @ A,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A] :
% 0.16/0.40 ( ( proces1525233512Action @ A @ X11 @ X122 )
% 0.16/0.40 != ( proces1915862579Choice @ A @ X212 @ X223 ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.distinct(1)
% 0.16/0.40 thf(fact_133_process_Oexhaust,axiom,
% 0.16/0.40 ! [A: $tType,Y3: proces634752977rocess @ A] :
% 0.16/0.40 ( ! [X113: A,X124: proces634752977rocess @ A] :
% 0.16/0.40 ( Y3
% 0.16/0.40 != ( proces1525233512Action @ A @ X113 @ X124 ) )
% 0.16/0.40 => ~ ! [X213: proces634752977rocess @ A,X224: proces634752977rocess @ A] :
% 0.16/0.40 ( Y3
% 0.16/0.40 != ( proces1915862579Choice @ A @ X213 @ X224 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.exhaust
% 0.16/0.40 thf(fact_134_process_Osel_I4_J,axiom,
% 0.16/0.40 ! [A: $tType,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A] :
% 0.16/0.40 ( ( proces988026546_ch2Of @ A @ ( proces1915862579Choice @ A @ X212 @ X223 ) )
% 0.16/0.40 = X223 ) ).
% 0.16/0.40
% 0.16/0.40 % process.sel(4)
% 0.16/0.40 thf(fact_135_process_Osel_I3_J,axiom,
% 0.16/0.40 ! [A: $tType,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A] :
% 0.16/0.40 ( ( proces979765041_ch1Of @ A @ ( proces1915862579Choice @ A @ X212 @ X223 ) )
% 0.16/0.40 = X212 ) ).
% 0.16/0.40
% 0.16/0.40 % process.sel(3)
% 0.16/0.40 thf(fact_136_process_Odistinct__disc_I2_J,axiom,
% 0.16/0.40 ! [A: $tType,Process: proces634752977rocess @ A] :
% 0.16/0.40 ( ( proces401113213Choice @ A @ Process )
% 0.16/0.40 => ~ ( proces10484146Action @ A @ Process ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.distinct_disc(2)
% 0.16/0.40 thf(fact_137_process_Odistinct__disc_I1_J,axiom,
% 0.16/0.40 ! [A: $tType,Process: proces634752977rocess @ A] :
% 0.16/0.40 ( ( proces10484146Action @ A @ Process )
% 0.16/0.40 => ~ ( proces401113213Choice @ A @ Process ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.distinct_disc(1)
% 0.16/0.40 thf(fact_138_isAction__isChoice,axiom,
% 0.16/0.40 ! [A: $tType,P: proces634752977rocess @ A] :
% 0.16/0.40 ( ( proces10484146Action @ A @ P )
% 0.16/0.40 | ( proces401113213Choice @ A @ P ) ) ).
% 0.16/0.40
% 0.16/0.40 % isAction_isChoice
% 0.16/0.40 thf(fact_139_process_Oexhaust__disc,axiom,
% 0.16/0.40 ! [A: $tType,Process: proces634752977rocess @ A] :
% 0.16/0.40 ( ~ ( proces10484146Action @ A @ Process )
% 0.16/0.40 => ( proces401113213Choice @ A @ Process ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.exhaust_disc
% 0.16/0.40 thf(fact_140_not__isAction__isChoice,axiom,
% 0.16/0.40 ! [A: $tType,P: proces634752977rocess @ A] :
% 0.16/0.40 ~ ( ( proces10484146Action @ A @ P )
% 0.16/0.40 & ( proces401113213Choice @ A @ P ) ) ).
% 0.16/0.40
% 0.16/0.40 % not_isAction_isChoice
% 0.16/0.40 thf(fact_141_process_Odisc_I3_J,axiom,
% 0.16/0.40 ! [A: $tType,X11: A,X122: proces634752977rocess @ A] :
% 0.16/0.40 ~ ( proces401113213Choice @ A @ ( proces1525233512Action @ A @ X11 @ X122 ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.disc(3)
% 0.16/0.40 thf(fact_142_process_Osimps_I6_J,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A] :
% 0.16/0.40 ( ( proces1406508781rocess @ A @ B @ F1 @ F2 @ ( proces1915862579Choice @ A @ X212 @ X223 ) )
% 0.16/0.40 = ( F2 @ X212 @ X223 ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.simps(6)
% 0.16/0.40 thf(fact_143_solution_Odisc_I2_J,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 0.16/0.40 ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 0.16/0.40 => ( proces401113213Choice @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % solution.disc(2)
% 0.16/0.40 thf(fact_144_process_Odisc__eq__case_I2_J,axiom,
% 0.16/0.40 ! [A: $tType] :
% 0.16/0.40 ( ( proces401113213Choice @ A )
% 0.16/0.40 = ( proces1406508781rocess @ A @ $o
% 0.16/0.40 @ ^ [Uu: A,Uv2: proces634752977rocess @ A] : $false
% 0.16/0.40 @ ^ [Uu: proces634752977rocess @ A,Uv2: proces634752977rocess @ A] : $true ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.disc_eq_case(2)
% 0.16/0.40 thf(fact_145_solution_Octr_I2_J,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 0.16/0.40 ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 0.16/0.40 => ( ( proces1652378886lution @ A @ B @ Sys @ T2 )
% 0.16/0.40 = ( proces1915862579Choice @ B @ ( proces1652378886lution @ A @ B @ Sys @ ( proces1239275103le_CH1 @ A @ B @ Sys @ T2 ) ) @ ( proces1652378886lution @ A @ B @ Sys @ ( proces1239275104le_CH2 @ A @ B @ Sys @ T2 ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % solution.ctr(2)
% 0.16/0.40 thf(fact_146_process_Oexhaust__sel,axiom,
% 0.16/0.40 ! [A: $tType,Process: proces634752977rocess @ A] :
% 0.16/0.40 ( ( Process
% 0.16/0.40 != ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) )
% 0.16/0.40 => ( Process
% 0.16/0.40 = ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.exhaust_sel
% 0.16/0.40 thf(fact_147_process_Ocoinduct__strong,axiom,
% 0.16/0.40 ! [A: $tType,R: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,Process: proces634752977rocess @ A,Process3: proces634752977rocess @ A] :
% 0.16/0.40 ( ( R @ Process @ Process3 )
% 0.16/0.40 => ( ! [Process4: proces634752977rocess @ A,Process5: proces634752977rocess @ A] :
% 0.16/0.40 ( ( R @ Process4 @ Process5 )
% 0.16/0.40 => ( ( ( proces10484146Action @ A @ Process4 )
% 0.16/0.40 = ( proces10484146Action @ A @ Process5 ) )
% 0.16/0.40 & ( ( proces10484146Action @ A @ Process4 )
% 0.16/0.40 => ( ( proces10484146Action @ A @ Process5 )
% 0.16/0.40 => ( ( ( proces745025900prefOf @ A @ Process4 )
% 0.16/0.40 = ( proces745025900prefOf @ A @ Process5 ) )
% 0.16/0.40 & ( ( R @ ( proces1778668539contOf @ A @ Process4 ) @ ( proces1778668539contOf @ A @ Process5 ) )
% 0.16/0.40 | ( ( proces1778668539contOf @ A @ Process4 )
% 0.16/0.40 = ( proces1778668539contOf @ A @ Process5 ) ) ) ) ) )
% 0.16/0.40 & ( ( proces401113213Choice @ A @ Process4 )
% 0.16/0.40 => ( ( proces401113213Choice @ A @ Process5 )
% 0.16/0.40 => ( ( ( R @ ( proces979765041_ch1Of @ A @ Process4 ) @ ( proces979765041_ch1Of @ A @ Process5 ) )
% 0.16/0.40 | ( ( proces979765041_ch1Of @ A @ Process4 )
% 0.16/0.40 = ( proces979765041_ch1Of @ A @ Process5 ) ) )
% 0.16/0.40 & ( ( R @ ( proces988026546_ch2Of @ A @ Process4 ) @ ( proces988026546_ch2Of @ A @ Process5 ) )
% 0.16/0.40 | ( ( proces988026546_ch2Of @ A @ Process4 )
% 0.16/0.40 = ( proces988026546_ch2Of @ A @ Process5 ) ) ) ) ) ) ) )
% 0.16/0.40 => ( Process = Process3 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.coinduct_strong
% 0.16/0.40 thf(fact_148_process_Orel__sel,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType] :
% 0.16/0.40 ( ( proces749077512rocess @ A @ B )
% 0.16/0.40 = ( ^ [R2: A > B > $o,A5: proces634752977rocess @ A,B5: proces634752977rocess @ B] :
% 0.16/0.40 ( ( ( proces10484146Action @ A @ A5 )
% 0.16/0.40 = ( proces10484146Action @ B @ B5 ) )
% 0.16/0.40 & ( ( proces10484146Action @ A @ A5 )
% 0.16/0.40 => ( ( proces10484146Action @ B @ B5 )
% 0.16/0.40 => ( ( R2 @ ( proces745025900prefOf @ A @ A5 ) @ ( proces745025900prefOf @ B @ B5 ) )
% 0.16/0.40 & ( proces749077512rocess @ A @ B @ R2 @ ( proces1778668539contOf @ A @ A5 ) @ ( proces1778668539contOf @ B @ B5 ) ) ) ) )
% 0.16/0.40 & ( ( proces401113213Choice @ A @ A5 )
% 0.16/0.40 => ( ( proces401113213Choice @ B @ B5 )
% 0.16/0.40 => ( ( proces749077512rocess @ A @ B @ R2 @ ( proces979765041_ch1Of @ A @ A5 ) @ ( proces979765041_ch1Of @ B @ B5 ) )
% 0.16/0.40 & ( proces749077512rocess @ A @ B @ R2 @ ( proces988026546_ch2Of @ A @ A5 ) @ ( proces988026546_ch2Of @ B @ B5 ) ) ) ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.rel_sel
% 0.16/0.40 thf(fact_149_process_Orel__coinduct,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,P3: ( proces634752977rocess @ A ) > ( proces634752977rocess @ B ) > $o,X7: proces634752977rocess @ A,Y3: proces634752977rocess @ B,R: A > B > $o] :
% 0.16/0.40 ( ( P3 @ X7 @ Y3 )
% 0.16/0.40 => ( ! [Process4: proces634752977rocess @ A,Process5: proces634752977rocess @ B] :
% 0.16/0.40 ( ( P3 @ Process4 @ Process5 )
% 0.16/0.40 => ( ( ( proces10484146Action @ A @ Process4 )
% 0.16/0.40 = ( proces10484146Action @ B @ Process5 ) )
% 0.16/0.40 & ( ( proces10484146Action @ A @ Process4 )
% 0.16/0.40 => ( ( proces10484146Action @ B @ Process5 )
% 0.16/0.40 => ( ( R @ ( proces745025900prefOf @ A @ Process4 ) @ ( proces745025900prefOf @ B @ Process5 ) )
% 0.16/0.40 & ( P3 @ ( proces1778668539contOf @ A @ Process4 ) @ ( proces1778668539contOf @ B @ Process5 ) ) ) ) )
% 0.16/0.40 & ( ( proces401113213Choice @ A @ Process4 )
% 0.16/0.40 => ( ( proces401113213Choice @ B @ Process5 )
% 0.16/0.40 => ( ( P3 @ ( proces979765041_ch1Of @ A @ Process4 ) @ ( proces979765041_ch1Of @ B @ Process5 ) )
% 0.16/0.40 & ( P3 @ ( proces988026546_ch2Of @ A @ Process4 ) @ ( proces988026546_ch2Of @ B @ Process5 ) ) ) ) ) ) )
% 0.16/0.40 => ( proces749077512rocess @ A @ B @ R @ X7 @ Y3 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.rel_coinduct
% 0.16/0.40 thf(fact_150_pred__equals__eq2,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
% 0.16/0.40 ( ( ( ^ [X: A,Y5: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y5 ) @ R ) )
% 0.16/0.40 = ( ^ [X: A,Y5: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y5 ) @ S ) ) )
% 0.16/0.40 = ( R = S ) ) ).
% 0.16/0.40
% 0.16/0.40 % pred_equals_eq2
% 0.16/0.40 thf(fact_151_internal__case__prod__conv,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,C: $tType,C3: B > C > A,A2: B,B2: C] :
% 0.16/0.40 ( ( produc2004651681e_prod @ B @ C @ A @ C3 @ ( product_Pair @ B @ C @ A2 @ B2 ) )
% 0.16/0.40 = ( C3 @ A2 @ B2 ) ) ).
% 0.16/0.40
% 0.16/0.40 % internal_case_prod_conv
% 0.16/0.40 thf(fact_152_process_Orel__inject_I1_J,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,R: A > B > $o,X11: A,X122: proces634752977rocess @ A,Y11: B,Y12: proces634752977rocess @ B] :
% 0.16/0.40 ( ( proces749077512rocess @ A @ B @ R @ ( proces1525233512Action @ A @ X11 @ X122 ) @ ( proces1525233512Action @ B @ Y11 @ Y12 ) )
% 0.16/0.40 = ( ( R @ X11 @ Y11 )
% 0.16/0.40 & ( proces749077512rocess @ A @ B @ R @ X122 @ Y12 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.rel_inject(1)
% 0.16/0.40 thf(fact_153_process_Orel__inject_I2_J,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,R: A > B > $o,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A,Y21: proces634752977rocess @ B,Y22: proces634752977rocess @ B] :
% 0.16/0.40 ( ( proces749077512rocess @ A @ B @ R @ ( proces1915862579Choice @ A @ X212 @ X223 ) @ ( proces1915862579Choice @ B @ Y21 @ Y22 ) )
% 0.16/0.40 = ( ( proces749077512rocess @ A @ B @ R @ X212 @ Y21 )
% 0.16/0.40 & ( proces749077512rocess @ A @ B @ R @ X223 @ Y22 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.rel_inject(2)
% 0.16/0.40 thf(fact_154_process_Orel__intros_I2_J,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,R: A > B > $o,X212: proces634752977rocess @ A,Y21: proces634752977rocess @ B,X223: proces634752977rocess @ A,Y22: proces634752977rocess @ B] :
% 0.16/0.40 ( ( proces749077512rocess @ A @ B @ R @ X212 @ Y21 )
% 0.16/0.40 => ( ( proces749077512rocess @ A @ B @ R @ X223 @ Y22 )
% 0.16/0.40 => ( proces749077512rocess @ A @ B @ R @ ( proces1915862579Choice @ A @ X212 @ X223 ) @ ( proces1915862579Choice @ B @ Y21 @ Y22 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.rel_intros(2)
% 0.16/0.40 thf(fact_155_process_Orel__refl,axiom,
% 0.16/0.40 ! [B: $tType,Ra: B > B > $o,X7: proces634752977rocess @ B] :
% 0.16/0.40 ( ! [X6: B] : ( Ra @ X6 @ X6 )
% 0.16/0.40 => ( proces749077512rocess @ B @ B @ Ra @ X7 @ X7 ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.rel_refl
% 0.16/0.40 thf(fact_156_process_Orel__eq,axiom,
% 0.16/0.40 ! [A: $tType] :
% 0.16/0.40 ( ( proces749077512rocess @ A @ A
% 0.16/0.40 @ ^ [Y6: A,Z: A] : ( Y6 = Z ) )
% 0.16/0.40 = ( ^ [Y6: proces634752977rocess @ A,Z: proces634752977rocess @ A] : ( Y6 = Z ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.rel_eq
% 0.16/0.40 thf(fact_157_process_Orel__intros_I1_J,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,R: A > B > $o,X11: A,Y11: B,X122: proces634752977rocess @ A,Y12: proces634752977rocess @ B] :
% 0.16/0.40 ( ( R @ X11 @ Y11 )
% 0.16/0.40 => ( ( proces749077512rocess @ A @ B @ R @ X122 @ Y12 )
% 0.16/0.40 => ( proces749077512rocess @ A @ B @ R @ ( proces1525233512Action @ A @ X11 @ X122 ) @ ( proces1525233512Action @ B @ Y11 @ Y12 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.rel_intros(1)
% 0.16/0.40 thf(fact_158_process_Orel__distinct_I2_J,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,R: A > B > $o,Y21: proces634752977rocess @ A,Y22: proces634752977rocess @ A,X11: B,X122: proces634752977rocess @ B] :
% 0.16/0.40 ~ ( proces749077512rocess @ A @ B @ R @ ( proces1915862579Choice @ A @ Y21 @ Y22 ) @ ( proces1525233512Action @ B @ X11 @ X122 ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.rel_distinct(2)
% 0.16/0.40 thf(fact_159_process_Orel__distinct_I1_J,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,R: A > B > $o,X11: A,X122: proces634752977rocess @ A,Y21: proces634752977rocess @ B,Y22: proces634752977rocess @ B] :
% 0.16/0.40 ~ ( proces749077512rocess @ A @ B @ R @ ( proces1525233512Action @ A @ X11 @ X122 ) @ ( proces1915862579Choice @ B @ Y21 @ Y22 ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.rel_distinct(1)
% 0.16/0.40 thf(fact_160_process_Orel__cases,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,R: A > B > $o,A2: proces634752977rocess @ A,B2: proces634752977rocess @ B] :
% 0.16/0.40 ( ( proces749077512rocess @ A @ B @ R @ A2 @ B2 )
% 0.16/0.40 => ( ! [X13: A,X23: proces634752977rocess @ A] :
% 0.16/0.40 ( ( A2
% 0.16/0.40 = ( proces1525233512Action @ A @ X13 @ X23 ) )
% 0.16/0.40 => ! [Y13: B,Y23: proces634752977rocess @ B] :
% 0.16/0.40 ( ( B2
% 0.16/0.40 = ( proces1525233512Action @ B @ Y13 @ Y23 ) )
% 0.16/0.40 => ( ( R @ X13 @ Y13 )
% 0.16/0.40 => ~ ( proces749077512rocess @ A @ B @ R @ X23 @ Y23 ) ) ) )
% 0.16/0.40 => ~ ! [X1a: proces634752977rocess @ A,X2a: proces634752977rocess @ A] :
% 0.16/0.40 ( ( A2
% 0.16/0.40 = ( proces1915862579Choice @ A @ X1a @ X2a ) )
% 0.16/0.40 => ! [Y1a: proces634752977rocess @ B,Y2a: proces634752977rocess @ B] :
% 0.16/0.40 ( ( B2
% 0.16/0.40 = ( proces1915862579Choice @ B @ Y1a @ Y2a ) )
% 0.16/0.40 => ( ( proces749077512rocess @ A @ B @ R @ X1a @ Y1a )
% 0.16/0.40 => ~ ( proces749077512rocess @ A @ B @ R @ X2a @ Y2a ) ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.rel_cases
% 0.16/0.40 thf(fact_161_process__term_Orel__induct,axiom,
% 0.16/0.40 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X7: proces554692349s_term @ A @ Pvar,Y3: proces554692349s_term @ B @ C,Q: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ B @ C ) > $o] :
% 0.16/0.40 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X7 @ Y3 )
% 0.16/0.40 => ( ! [A12: Pvar,B1: C] :
% 0.16/0.40 ( ( R22 @ A12 @ B1 )
% 0.16/0.40 => ( Q @ ( proces1627516585ss_VAR @ Pvar @ A @ A12 ) @ ( proces1627516585ss_VAR @ C @ B @ B1 ) ) )
% 0.16/0.40 => ( ! [A22: proces634752977rocess @ A,B22: proces634752977rocess @ B] :
% 0.16/0.40 ( ( proces749077512rocess @ A @ B @ R1 @ A22 @ B22 )
% 0.16/0.40 => ( Q @ ( proces1062592052s_PROC @ A @ Pvar @ A22 ) @ ( proces1062592052s_PROC @ B @ C @ B22 ) ) )
% 0.16/0.40 => ( ! [A31: A,A32: proces554692349s_term @ A @ Pvar,B31: B,B32: proces554692349s_term @ B @ C] :
% 0.16/0.40 ( ( R1 @ A31 @ B31 )
% 0.16/0.40 => ( ( Q @ A32 @ B32 )
% 0.16/0.40 => ( Q @ ( proces1454156180ss_ACT @ A @ Pvar @ A31 @ A32 ) @ ( proces1454156180ss_ACT @ B @ C @ B31 @ B32 ) ) ) )
% 0.16/0.40 => ( ! [A41: proces554692349s_term @ A @ Pvar,A42: proces554692349s_term @ A @ Pvar,B41: proces554692349s_term @ B @ C,B42: proces554692349s_term @ B @ C] :
% 0.16/0.40 ( ( Q @ A41 @ B41 )
% 0.16/0.40 => ( ( Q @ A42 @ B42 )
% 0.16/0.40 => ( Q @ ( proces89589571ess_CH @ A @ Pvar @ A41 @ A42 ) @ ( proces89589571ess_CH @ B @ C @ B41 @ B42 ) ) ) )
% 0.16/0.40 => ( Q @ X7 @ Y3 ) ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_term.rel_induct
% 0.16/0.40 thf(fact_162_process__term_Orel__cases,axiom,
% 0.16/0.40 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,A2: proces554692349s_term @ A @ Pvar,B2: proces554692349s_term @ B @ C] :
% 0.16/0.40 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ A2 @ B2 )
% 0.16/0.40 => ( ! [X6: Pvar] :
% 0.16/0.40 ( ( A2
% 0.16/0.40 = ( proces1627516585ss_VAR @ Pvar @ A @ X6 ) )
% 0.16/0.40 => ! [Y4: C] :
% 0.16/0.40 ( ( B2
% 0.16/0.40 = ( proces1627516585ss_VAR @ C @ B @ Y4 ) )
% 0.16/0.40 => ~ ( R22 @ X6 @ Y4 ) ) )
% 0.16/0.40 => ( ! [Xa2: proces634752977rocess @ A] :
% 0.16/0.40 ( ( A2
% 0.16/0.40 = ( proces1062592052s_PROC @ A @ Pvar @ Xa2 ) )
% 0.16/0.40 => ! [Ya: proces634752977rocess @ B] :
% 0.16/0.40 ( ( B2
% 0.16/0.40 = ( proces1062592052s_PROC @ B @ C @ Ya ) )
% 0.16/0.40 => ~ ( proces749077512rocess @ A @ B @ R1 @ Xa2 @ Ya ) ) )
% 0.16/0.40 => ( ! [X1a: A,X2a: proces554692349s_term @ A @ Pvar] :
% 0.16/0.40 ( ( A2
% 0.16/0.40 = ( proces1454156180ss_ACT @ A @ Pvar @ X1a @ X2a ) )
% 0.16/0.40 => ! [Y1a: B,Y2a: proces554692349s_term @ B @ C] :
% 0.16/0.40 ( ( B2
% 0.16/0.40 = ( proces1454156180ss_ACT @ B @ C @ Y1a @ Y2a ) )
% 0.16/0.40 => ( ( R1 @ X1a @ Y1a )
% 0.16/0.40 => ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X2a @ Y2a ) ) ) )
% 0.16/0.40 => ~ ! [X1b: proces554692349s_term @ A @ Pvar,X2b: proces554692349s_term @ A @ Pvar] :
% 0.16/0.40 ( ( A2
% 0.16/0.40 = ( proces89589571ess_CH @ A @ Pvar @ X1b @ X2b ) )
% 0.16/0.40 => ! [Y1b: proces554692349s_term @ B @ C,Y2b: proces554692349s_term @ B @ C] :
% 0.16/0.40 ( ( B2
% 0.16/0.40 = ( proces89589571ess_CH @ B @ C @ Y1b @ Y2b ) )
% 0.16/0.40 => ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X1b @ Y1b )
% 0.16/0.40 => ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X2b @ Y2b ) ) ) ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_term.rel_cases
% 0.16/0.40 thf(fact_163_process__term_Oset__cases_I2_J,axiom,
% 0.16/0.40 ! [Pvar: $tType,A: $tType,E3: Pvar,A2: proces554692349s_term @ A @ Pvar] :
% 0.16/0.40 ( ( member @ Pvar @ E3 @ ( proces1493547885s_term @ A @ Pvar @ A2 ) )
% 0.16/0.40 => ( ( A2
% 0.16/0.40 != ( proces1627516585ss_VAR @ Pvar @ A @ E3 ) )
% 0.16/0.40 => ( ! [Z1: A,Z2: proces554692349s_term @ A @ Pvar] :
% 0.16/0.40 ( ( A2
% 0.16/0.40 = ( proces1454156180ss_ACT @ A @ Pvar @ Z1 @ Z2 ) )
% 0.16/0.40 => ~ ( member @ Pvar @ E3 @ ( proces1493547885s_term @ A @ Pvar @ Z2 ) ) )
% 0.16/0.40 => ( ! [Z1: proces554692349s_term @ A @ Pvar] :
% 0.16/0.40 ( ? [Z2: proces554692349s_term @ A @ Pvar] :
% 0.16/0.40 ( A2
% 0.16/0.40 = ( proces89589571ess_CH @ A @ Pvar @ Z1 @ Z2 ) )
% 0.16/0.40 => ~ ( member @ Pvar @ E3 @ ( proces1493547885s_term @ A @ Pvar @ Z1 ) ) )
% 0.16/0.40 => ~ ! [Z1: proces554692349s_term @ A @ Pvar,Z2: proces554692349s_term @ A @ Pvar] :
% 0.16/0.40 ( ( A2
% 0.16/0.40 = ( proces89589571ess_CH @ A @ Pvar @ Z1 @ Z2 ) )
% 0.16/0.40 => ~ ( member @ Pvar @ E3 @ ( proces1493547885s_term @ A @ Pvar @ Z2 ) ) ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_term.set_cases(2)
% 0.16/0.40 thf(fact_164_process__term_Oset__intros_I6_J,axiom,
% 0.16/0.40 ! [A: $tType,Pvar: $tType,Ab2: Pvar] : ( member @ Pvar @ Ab2 @ ( proces1493547885s_term @ A @ Pvar @ ( proces1627516585ss_VAR @ Pvar @ A @ Ab2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_term.set_intros(6)
% 0.16/0.40 thf(fact_165_process__term_Oset__intros_I8_J,axiom,
% 0.16/0.40 ! [Pvar: $tType,A: $tType,Xk: Pvar,A1c: proces554692349s_term @ A @ Pvar,A2c: proces554692349s_term @ A @ Pvar] :
% 0.16/0.40 ( ( member @ Pvar @ Xk @ ( proces1493547885s_term @ A @ Pvar @ A1c ) )
% 0.16/0.40 => ( member @ Pvar @ Xk @ ( proces1493547885s_term @ A @ Pvar @ ( proces89589571ess_CH @ A @ Pvar @ A1c @ A2c ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_term.set_intros(8)
% 0.16/0.40 thf(fact_166_process__term_Oset__intros_I9_J,axiom,
% 0.16/0.40 ! [Pvar: $tType,A: $tType,Xm: Pvar,A2c: proces554692349s_term @ A @ Pvar,A1c: proces554692349s_term @ A @ Pvar] :
% 0.16/0.40 ( ( member @ Pvar @ Xm @ ( proces1493547885s_term @ A @ Pvar @ A2c ) )
% 0.16/0.40 => ( member @ Pvar @ Xm @ ( proces1493547885s_term @ A @ Pvar @ ( proces89589571ess_CH @ A @ Pvar @ A1c @ A2c ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_term.set_intros(9)
% 0.16/0.40 thf(fact_167_process__term_Oset__intros_I7_J,axiom,
% 0.16/0.40 ! [Pvar: $tType,A: $tType,Xi: Pvar,A2b: proces554692349s_term @ A @ Pvar,A1b: A] :
% 0.16/0.40 ( ( member @ Pvar @ Xi @ ( proces1493547885s_term @ A @ Pvar @ A2b ) )
% 0.16/0.40 => ( member @ Pvar @ Xi @ ( proces1493547885s_term @ A @ Pvar @ ( proces1454156180ss_ACT @ A @ Pvar @ A1b @ A2b ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_term.set_intros(7)
% 0.16/0.40 thf(fact_168_process__term_Osimps_I51_J,axiom,
% 0.16/0.40 ! [Pvar: $tType,A: $tType,X31: A,X32: proces554692349s_term @ A @ Pvar] :
% 0.16/0.40 ( ( proces1493547885s_term @ A @ Pvar @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) )
% 0.16/0.40 = ( proces1493547885s_term @ A @ Pvar @ X32 ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_term.simps(51)
% 0.16/0.40 thf(fact_169_process__term_Orel__intros_I1_J,axiom,
% 0.16/0.40 ! [Pvar: $tType,A: $tType,B: $tType,C: $tType,R22: Pvar > C > $o,X1: Pvar,Y1: C,R1: A > B > $o] :
% 0.16/0.40 ( ( R22 @ X1 @ Y1 )
% 0.16/0.40 => ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) @ ( proces1627516585ss_VAR @ C @ B @ Y1 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_term.rel_intros(1)
% 0.16/0.40 thf(fact_170_process__term_Orel__inject_I1_J,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,Pvar: $tType,C: $tType,R1: A > B > $o,R22: Pvar > C > $o,X1: Pvar,Y1: C] :
% 0.16/0.40 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) @ ( proces1627516585ss_VAR @ C @ B @ Y1 ) )
% 0.16/0.40 = ( R22 @ X1 @ Y1 ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_term.rel_inject(1)
% 0.16/0.40 thf(fact_171_process__term_Orel__intros_I4_J,axiom,
% 0.16/0.40 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X41: proces554692349s_term @ A @ Pvar,Y41: proces554692349s_term @ B @ C,X42: proces554692349s_term @ A @ Pvar,Y42: proces554692349s_term @ B @ C] :
% 0.16/0.40 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X41 @ Y41 )
% 0.16/0.40 => ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X42 @ Y42 )
% 0.16/0.40 => ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_term.rel_intros(4)
% 0.16/0.40 thf(fact_172_process__term_Orel__inject_I4_J,axiom,
% 0.16/0.40 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar,Y41: proces554692349s_term @ B @ C,Y42: proces554692349s_term @ B @ C] :
% 0.16/0.40 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) )
% 0.16/0.40 = ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X41 @ Y41 )
% 0.16/0.40 & ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X42 @ Y42 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_term.rel_inject(4)
% 0.16/0.40 thf(fact_173_process__term_Orel__intros_I3_J,axiom,
% 0.16/0.40 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,X31: A,Y31: B,R22: Pvar > C > $o,X32: proces554692349s_term @ A @ Pvar,Y32: proces554692349s_term @ B @ C] :
% 0.16/0.40 ( ( R1 @ X31 @ Y31 )
% 0.16/0.40 => ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X32 @ Y32 )
% 0.16/0.40 => ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_term.rel_intros(3)
% 0.16/0.40 thf(fact_174_process__term_Orel__inject_I3_J,axiom,
% 0.16/0.40 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X31: A,X32: proces554692349s_term @ A @ Pvar,Y31: B,Y32: proces554692349s_term @ B @ C] :
% 0.16/0.40 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) )
% 0.16/0.40 = ( ( R1 @ X31 @ Y31 )
% 0.16/0.40 & ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X32 @ Y32 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_term.rel_inject(3)
% 0.16/0.40 thf(fact_175_process__term_Orel__eq,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType] :
% 0.16/0.40 ( ( proces2029722208s_term @ A @ A @ B @ B
% 0.16/0.40 @ ^ [Y6: A,Z: A] : ( Y6 = Z )
% 0.16/0.40 @ ^ [Y6: B,Z: B] : ( Y6 = Z ) )
% 0.16/0.40 = ( ^ [Y6: proces554692349s_term @ A @ B,Z: proces554692349s_term @ A @ B] : ( Y6 = Z ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_term.rel_eq
% 0.16/0.40 thf(fact_176_process__term_Orel__refl,axiom,
% 0.16/0.40 ! [D: $tType,C: $tType,R1a: C > C > $o,R2a: D > D > $o,X7: proces554692349s_term @ C @ D] :
% 0.16/0.40 ( ! [X6: C] : ( R1a @ X6 @ X6 )
% 0.16/0.40 => ( ! [X6: D] : ( R2a @ X6 @ X6 )
% 0.16/0.40 => ( proces2029722208s_term @ C @ C @ D @ D @ R1a @ R2a @ X7 @ X7 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_term.rel_refl
% 0.16/0.40 thf(fact_177_process__term_Orel__inject_I2_J,axiom,
% 0.16/0.40 ! [C: $tType,Pvar: $tType,A: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X2: proces634752977rocess @ A,Y2: proces634752977rocess @ B] :
% 0.16/0.40 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) @ ( proces1062592052s_PROC @ B @ C @ Y2 ) )
% 0.16/0.40 = ( proces749077512rocess @ A @ B @ R1 @ X2 @ Y2 ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_term.rel_inject(2)
% 0.16/0.40 thf(fact_178_process__term_Orel__intros_I2_J,axiom,
% 0.16/0.40 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,X2: proces634752977rocess @ A,Y2: proces634752977rocess @ B,R22: Pvar > C > $o] :
% 0.16/0.40 ( ( proces749077512rocess @ A @ B @ R1 @ X2 @ Y2 )
% 0.16/0.40 => ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) @ ( proces1062592052s_PROC @ B @ C @ Y2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_term.rel_intros(2)
% 0.16/0.40 thf(fact_179_process__term_Orel__distinct_I1_J,axiom,
% 0.16/0.40 ! [Pvar: $tType,A: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X1: Pvar,Y2: proces634752977rocess @ B] :
% 0.16/0.40 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) @ ( proces1062592052s_PROC @ B @ C @ Y2 ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_term.rel_distinct(1)
% 0.16/0.40 thf(fact_180_process__term_Orel__distinct_I2_J,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,C: $tType,D: $tType,R1: A > C > $o,R22: B > D > $o,Y2: proces634752977rocess @ A,X1: D] :
% 0.16/0.40 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ B @ Y2 ) @ ( proces1627516585ss_VAR @ D @ C @ X1 ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_term.rel_distinct(2)
% 0.16/0.40 thf(fact_181_process__term_Orel__distinct_I9_J,axiom,
% 0.16/0.40 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X2: proces634752977rocess @ A,Y41: proces554692349s_term @ B @ C,Y42: proces554692349s_term @ B @ C] :
% 0.16/0.40 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_term.rel_distinct(9)
% 0.16/0.40 thf(fact_182_process__term_Orel__distinct_I10_J,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: B > D > $o,Y41: proces554692349s_term @ A @ B,Y42: proces554692349s_term @ A @ B,X2: proces634752977rocess @ C] :
% 0.16/0.40 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces89589571ess_CH @ A @ B @ Y41 @ Y42 ) @ ( proces1062592052s_PROC @ C @ D @ X2 ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_term.rel_distinct(10)
% 0.16/0.40 thf(fact_183_process__term_Orel__distinct_I7_J,axiom,
% 0.16/0.40 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X2: proces634752977rocess @ A,Y31: B,Y32: proces554692349s_term @ B @ C] :
% 0.16/0.40 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_term.rel_distinct(7)
% 0.16/0.40 thf(fact_184_process__term_Orel__distinct_I8_J,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: B > D > $o,Y31: A,Y32: proces554692349s_term @ A @ B,X2: proces634752977rocess @ C] :
% 0.16/0.40 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ B @ Y31 @ Y32 ) @ ( proces1062592052s_PROC @ C @ D @ X2 ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_term.rel_distinct(8)
% 0.16/0.40 thf(fact_185_process__term_Orel__distinct_I6_J,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,C: $tType,D: $tType,R1: A > C > $o,R22: B > D > $o,Y41: proces554692349s_term @ A @ B,Y42: proces554692349s_term @ A @ B,X1: D] :
% 0.16/0.40 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces89589571ess_CH @ A @ B @ Y41 @ Y42 ) @ ( proces1627516585ss_VAR @ D @ C @ X1 ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_term.rel_distinct(6)
% 0.16/0.40 thf(fact_186_process__term_Orel__distinct_I5_J,axiom,
% 0.16/0.40 ! [Pvar: $tType,A: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X1: Pvar,Y41: proces554692349s_term @ B @ C,Y42: proces554692349s_term @ B @ C] :
% 0.16/0.40 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_term.rel_distinct(5)
% 0.16/0.40 thf(fact_187_process__term_Orel__distinct_I4_J,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,C: $tType,D: $tType,R1: A > C > $o,R22: B > D > $o,Y31: A,Y32: proces554692349s_term @ A @ B,X1: D] :
% 0.16/0.40 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ B @ Y31 @ Y32 ) @ ( proces1627516585ss_VAR @ D @ C @ X1 ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_term.rel_distinct(4)
% 0.16/0.40 thf(fact_188_process__term_Orel__distinct_I3_J,axiom,
% 0.16/0.40 ! [Pvar: $tType,A: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X1: Pvar,Y31: B,Y32: proces554692349s_term @ B @ C] :
% 0.16/0.40 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_term.rel_distinct(3)
% 0.16/0.40 thf(fact_189_process__term_Orel__distinct_I12_J,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: B > D > $o,Y41: proces554692349s_term @ A @ B,Y42: proces554692349s_term @ A @ B,X31: C,X32: proces554692349s_term @ C @ D] :
% 0.16/0.40 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces89589571ess_CH @ A @ B @ Y41 @ Y42 ) @ ( proces1454156180ss_ACT @ C @ D @ X31 @ X32 ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_term.rel_distinct(12)
% 0.16/0.40 thf(fact_190_process__term_Orel__distinct_I11_J,axiom,
% 0.16/0.40 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X31: A,X32: proces554692349s_term @ A @ Pvar,Y41: proces554692349s_term @ B @ C,Y42: proces554692349s_term @ B @ C] :
% 0.16/0.40 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_term.rel_distinct(11)
% 0.16/0.40 thf(fact_191_accp_Ocases,axiom,
% 0.16/0.40 ! [A: $tType,R3: A > A > $o,A2: A] :
% 0.16/0.40 ( ( accp @ A @ R3 @ A2 )
% 0.16/0.40 => ! [Y7: A] :
% 0.16/0.40 ( ( R3 @ Y7 @ A2 )
% 0.16/0.40 => ( accp @ A @ R3 @ Y7 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % accp.cases
% 0.16/0.40 thf(fact_192_accp_Osimps,axiom,
% 0.16/0.40 ! [A: $tType] :
% 0.16/0.40 ( ( accp @ A )
% 0.16/0.40 = ( ^ [R4: A > A > $o,A5: A] :
% 0.16/0.40 ? [X: A] :
% 0.16/0.40 ( ( A5 = X )
% 0.16/0.40 & ! [Y5: A] :
% 0.16/0.40 ( ( R4 @ Y5 @ X )
% 0.16/0.40 => ( accp @ A @ R4 @ Y5 ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % accp.simps
% 0.16/0.40 thf(fact_193_accp_Ointros,axiom,
% 0.16/0.40 ! [A: $tType,R3: A > A > $o,X7: A] :
% 0.16/0.40 ( ! [Y4: A] :
% 0.16/0.40 ( ( R3 @ Y4 @ X7 )
% 0.16/0.40 => ( accp @ A @ R3 @ Y4 ) )
% 0.16/0.40 => ( accp @ A @ R3 @ X7 ) ) ).
% 0.16/0.40
% 0.16/0.40 % accp.intros
% 0.16/0.40 thf(fact_194_accp__induct__rule,axiom,
% 0.16/0.40 ! [A: $tType,R3: A > A > $o,A2: A,P3: A > $o] :
% 0.16/0.40 ( ( accp @ A @ R3 @ A2 )
% 0.16/0.40 => ( ! [X6: A] :
% 0.16/0.40 ( ( accp @ A @ R3 @ X6 )
% 0.16/0.40 => ( ! [Y7: A] :
% 0.16/0.40 ( ( R3 @ Y7 @ X6 )
% 0.16/0.40 => ( P3 @ Y7 ) )
% 0.16/0.40 => ( P3 @ X6 ) ) )
% 0.16/0.40 => ( P3 @ A2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % accp_induct_rule
% 0.16/0.40 thf(fact_195_not__accp__down,axiom,
% 0.16/0.40 ! [A: $tType,R: A > A > $o,X7: A] :
% 0.16/0.40 ( ~ ( accp @ A @ R @ X7 )
% 0.16/0.40 => ~ ! [Z3: A] :
% 0.16/0.40 ( ( R @ Z3 @ X7 )
% 0.16/0.40 => ( accp @ A @ R @ Z3 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % not_accp_down
% 0.16/0.40 thf(fact_196_accp__downward,axiom,
% 0.16/0.40 ! [A: $tType,R3: A > A > $o,B2: A,A2: A] :
% 0.16/0.40 ( ( accp @ A @ R3 @ B2 )
% 0.16/0.40 => ( ( R3 @ A2 @ B2 )
% 0.16/0.40 => ( accp @ A @ R3 @ A2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % accp_downward
% 0.16/0.40 thf(fact_197_accp_Oinducts,axiom,
% 0.16/0.40 ! [A: $tType,R3: A > A > $o,X7: A,P3: A > $o] :
% 0.16/0.40 ( ( accp @ A @ R3 @ X7 )
% 0.16/0.40 => ( ! [X6: A] :
% 0.16/0.40 ( ! [Y7: A] :
% 0.16/0.40 ( ( R3 @ Y7 @ X6 )
% 0.16/0.40 => ( accp @ A @ R3 @ Y7 ) )
% 0.16/0.40 => ( ! [Y7: A] :
% 0.16/0.40 ( ( R3 @ Y7 @ X6 )
% 0.16/0.40 => ( P3 @ Y7 ) )
% 0.16/0.40 => ( P3 @ X6 ) ) )
% 0.16/0.40 => ( P3 @ X7 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % accp.inducts
% 0.16/0.40 thf(fact_198_accp__induct,axiom,
% 0.16/0.40 ! [A: $tType,R3: A > A > $o,A2: A,P3: A > $o] :
% 0.16/0.40 ( ( accp @ A @ R3 @ A2 )
% 0.16/0.40 => ( ! [X6: A] :
% 0.16/0.40 ( ( accp @ A @ R3 @ X6 )
% 0.16/0.40 => ( ! [Y7: A] :
% 0.16/0.40 ( ( R3 @ Y7 @ X6 )
% 0.16/0.40 => ( P3 @ Y7 ) )
% 0.16/0.40 => ( P3 @ X6 ) ) )
% 0.16/0.40 => ( P3 @ A2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % accp_induct
% 0.16/0.40 thf(fact_199_in__lex__prod,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,A2: A,B2: B,A6: A,B3: B,R3: set @ ( product_prod @ A @ A ),S2: set @ ( product_prod @ B @ B )] :
% 0.16/0.40 ( ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A2 @ B2 ) @ ( product_Pair @ A @ B @ A6 @ B3 ) ) @ ( lex_prod @ A @ B @ R3 @ S2 ) )
% 0.16/0.40 = ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ A6 ) @ R3 )
% 0.16/0.40 | ( ( A2 = A6 )
% 0.16/0.40 & ( member @ ( product_prod @ B @ B ) @ ( product_Pair @ B @ B @ B2 @ B3 ) @ S2 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % in_lex_prod
% 0.16/0.40 thf(fact_200_process_Ocorec__code,axiom,
% 0.16/0.40 ! [A: $tType,C: $tType] :
% 0.16/0.40 ( ( proces894737309rocess @ C @ A )
% 0.16/0.40 = ( ^ [P5: C > $o,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C,A5: C] : ( if @ ( proces634752977rocess @ A ) @ ( P5 @ A5 ) @ ( proces1525233512Action @ A @ ( G11 @ A5 ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q12 @ A5 ) @ ( G121 @ A5 ) @ ( proces894737309rocess @ C @ A @ P5 @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G122 @ A5 ) ) ) ) @ ( proces1915862579Choice @ A @ ( if @ ( proces634752977rocess @ A ) @ ( Q21 @ A5 ) @ ( G211 @ A5 ) @ ( proces894737309rocess @ C @ A @ P5 @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G212 @ A5 ) ) ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q22 @ A5 ) @ ( G221 @ A5 ) @ ( proces894737309rocess @ C @ A @ P5 @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G222 @ A5 ) ) ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.corec_code
% 0.16/0.40 thf(fact_201_process_Ocorec__disc__iff_I1_J,axiom,
% 0.16/0.40 ! [A: $tType,C: $tType,P: C > $o,G112: C > A,Q122: C > $o,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,Q212: C > $o,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,Q222: C > $o,G2212: C > ( proces634752977rocess @ A ),G2222: C > C,A2: C] :
% 0.16/0.40 ( ( proces10484146Action @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 0.16/0.40 = ( P @ A2 ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.corec_disc_iff(1)
% 0.16/0.40 thf(fact_202_process_Ocorec__disc__iff_I2_J,axiom,
% 0.16/0.40 ! [A: $tType,C: $tType,P: C > $o,G112: C > A,Q122: C > $o,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,Q212: C > $o,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,Q222: C > $o,G2212: C > ( proces634752977rocess @ A ),G2222: C > C,A2: C] :
% 0.16/0.40 ( ( proces401113213Choice @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 0.16/0.40 = ( ~ ( P @ A2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.corec_disc_iff(2)
% 0.16/0.40 thf(fact_203_process_Ocorec__disc_I1_J,axiom,
% 0.16/0.40 ! [A: $tType,C: $tType,P: C > $o,A2: C,G112: C > A,Q122: C > $o,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,Q212: C > $o,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,Q222: C > $o,G2212: C > ( proces634752977rocess @ A ),G2222: C > C] :
% 0.16/0.40 ( ( P @ A2 )
% 0.16/0.40 => ( proces10484146Action @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.corec_disc(1)
% 0.16/0.40 thf(fact_204_process_Ocorec_I1_J,axiom,
% 0.16/0.40 ! [A: $tType,C: $tType,P: C > $o,A2: C,G112: C > A,Q122: C > $o,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,Q212: C > $o,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,Q222: C > $o,G2212: C > ( proces634752977rocess @ A ),G2222: C > C] :
% 0.16/0.40 ( ( P @ A2 )
% 0.16/0.40 => ( ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 )
% 0.16/0.40 = ( proces1525233512Action @ A @ ( G112 @ A2 ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q122 @ A2 ) @ ( G1212 @ A2 ) @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G1222 @ A2 ) ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.corec(1)
% 0.16/0.40 thf(fact_205_process_Ocorec_I2_J,axiom,
% 0.16/0.40 ! [A: $tType,C: $tType,P: C > $o,A2: C,G112: C > A,Q122: C > $o,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,Q212: C > $o,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,Q222: C > $o,G2212: C > ( proces634752977rocess @ A ),G2222: C > C] :
% 0.16/0.40 ( ~ ( P @ A2 )
% 0.16/0.40 => ( ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 )
% 0.16/0.40 = ( proces1915862579Choice @ A @ ( if @ ( proces634752977rocess @ A ) @ ( Q212 @ A2 ) @ ( G2112 @ A2 ) @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G2122 @ A2 ) ) ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q222 @ A2 ) @ ( G2212 @ A2 ) @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G2222 @ A2 ) ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.corec(2)
% 0.16/0.40 thf(fact_206_process_Ocorec__disc_I2_J,axiom,
% 0.16/0.40 ! [A: $tType,C: $tType,P: C > $o,A2: C,G112: C > A,Q122: C > $o,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,Q212: C > $o,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,Q222: C > $o,G2212: C > ( proces634752977rocess @ A ),G2222: C > C] :
% 0.16/0.40 ( ~ ( P @ A2 )
% 0.16/0.40 => ( proces401113213Choice @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.corec_disc(2)
% 0.16/0.40 thf(fact_207_process_Ocorec__sel_I2_J,axiom,
% 0.16/0.40 ! [A: $tType,C: $tType,P: C > $o,A2: C,Q122: C > $o,G112: C > A,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,Q212: C > $o,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,Q222: C > $o,G2212: C > ( proces634752977rocess @ A ),G2222: C > C] :
% 0.16/0.40 ( ( P @ A2 )
% 0.16/0.40 => ( ( ( Q122 @ A2 )
% 0.16/0.40 => ( ( proces1778668539contOf @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 0.16/0.40 = ( G1212 @ A2 ) ) )
% 0.16/0.40 & ( ~ ( Q122 @ A2 )
% 0.16/0.40 => ( ( proces1778668539contOf @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 0.16/0.40 = ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G1222 @ A2 ) ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.corec_sel(2)
% 0.16/0.40 thf(fact_208_process_Ocorec__sel_I3_J,axiom,
% 0.16/0.40 ! [A: $tType,C: $tType,P: C > $o,A2: C,Q212: C > $o,G112: C > A,Q122: C > $o,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,Q222: C > $o,G2212: C > ( proces634752977rocess @ A ),G2222: C > C] :
% 0.16/0.40 ( ~ ( P @ A2 )
% 0.16/0.40 => ( ( ( Q212 @ A2 )
% 0.16/0.40 => ( ( proces979765041_ch1Of @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 0.16/0.40 = ( G2112 @ A2 ) ) )
% 0.16/0.40 & ( ~ ( Q212 @ A2 )
% 0.16/0.40 => ( ( proces979765041_ch1Of @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 0.16/0.40 = ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G2122 @ A2 ) ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.corec_sel(3)
% 0.16/0.40 thf(fact_209_process_Ocorec__sel_I4_J,axiom,
% 0.16/0.40 ! [A: $tType,C: $tType,P: C > $o,A2: C,Q222: C > $o,G112: C > A,Q122: C > $o,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,Q212: C > $o,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,G2212: C > ( proces634752977rocess @ A ),G2222: C > C] :
% 0.16/0.40 ( ~ ( P @ A2 )
% 0.16/0.40 => ( ( ( Q222 @ A2 )
% 0.16/0.40 => ( ( proces988026546_ch2Of @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 0.16/0.40 = ( G2212 @ A2 ) ) )
% 0.16/0.40 & ( ~ ( Q222 @ A2 )
% 0.16/0.40 => ( ( proces988026546_ch2Of @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 0.16/0.40 = ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G2222 @ A2 ) ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.corec_sel(4)
% 0.16/0.40 thf(fact_210_process_Ocorec__sel_I1_J,axiom,
% 0.16/0.40 ! [A: $tType,C: $tType,P: C > $o,A2: C,G112: C > A,Q122: C > $o,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,Q212: C > $o,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,Q222: C > $o,G2212: C > ( proces634752977rocess @ A ),G2222: C > C] :
% 0.16/0.40 ( ( P @ A2 )
% 0.16/0.40 => ( ( proces745025900prefOf @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 0.16/0.40 = ( G112 @ A2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.corec_sel(1)
% 0.16/0.40 thf(fact_211_same__fstI,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,P3: A > $o,X7: A,Y8: B,Y3: B,R: A > ( set @ ( product_prod @ B @ B ) )] :
% 0.16/0.40 ( ( P3 @ X7 )
% 0.16/0.40 => ( ( member @ ( product_prod @ B @ B ) @ ( product_Pair @ B @ B @ Y8 @ Y3 ) @ ( R @ X7 ) )
% 0.16/0.40 => ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X7 @ Y8 ) @ ( product_Pair @ A @ B @ X7 @ Y3 ) ) @ ( same_fst @ A @ B @ P3 @ R ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % same_fstI
% 0.16/0.40 thf(fact_212_ssubst__Pair__rhs,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,R3: A,S2: B,R: set @ ( product_prod @ A @ B ),S3: B] :
% 0.16/0.40 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R3 @ S2 ) @ R )
% 0.16/0.40 => ( ( S3 = S2 )
% 0.16/0.40 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R3 @ S3 ) @ R ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % ssubst_Pair_rhs
% 0.16/0.40 thf(fact_213_cut__def,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType] :
% 0.16/0.40 ( ( cut @ A @ B )
% 0.16/0.40 = ( ^ [F7: A > B,R2: set @ ( product_prod @ A @ A ),X: A,Y5: A] : ( if @ B @ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y5 @ X ) @ R2 ) @ ( F7 @ Y5 ) @ ( undefined @ B ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % cut_def
% 0.16/0.40 thf(fact_214_curry__conv,axiom,
% 0.16/0.40 ! [A: $tType,C: $tType,B: $tType] :
% 0.16/0.40 ( ( product_curry @ B @ C @ A )
% 0.16/0.40 = ( ^ [F7: ( product_prod @ B @ C ) > A,A5: B,B5: C] : ( F7 @ ( product_Pair @ B @ C @ A5 @ B5 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % curry_conv
% 0.16/0.40 thf(fact_215_curryI,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,F: ( product_prod @ A @ B ) > $o,A2: A,B2: B] :
% 0.16/0.40 ( ( F @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.16/0.40 => ( product_curry @ A @ B @ $o @ F @ A2 @ B2 ) ) ).
% 0.16/0.40
% 0.16/0.40 % curryI
% 0.16/0.40 thf(fact_216_cuts__eq,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,F: A > B,R: set @ ( product_prod @ A @ A ),X7: A,G: A > B] :
% 0.16/0.40 ( ( ( cut @ A @ B @ F @ R @ X7 )
% 0.16/0.40 = ( cut @ A @ B @ G @ R @ X7 ) )
% 0.16/0.40 = ( ! [Y5: A] :
% 0.16/0.40 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y5 @ X7 ) @ R )
% 0.16/0.40 => ( ( F @ Y5 )
% 0.16/0.40 = ( G @ Y5 ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % cuts_eq
% 0.16/0.40 thf(fact_217_cut__apply,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,X7: A,A2: A,R: set @ ( product_prod @ A @ A ),F: A > B] :
% 0.16/0.40 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X7 @ A2 ) @ R )
% 0.16/0.40 => ( ( cut @ A @ B @ F @ R @ A2 @ X7 )
% 0.16/0.40 = ( F @ X7 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % cut_apply
% 0.16/0.40 thf(fact_218_curry__K,axiom,
% 0.16/0.40 ! [B: $tType,C: $tType,A: $tType,C3: C] :
% 0.16/0.40 ( ( product_curry @ A @ B @ C
% 0.16/0.40 @ ^ [X: product_prod @ A @ B] : C3 )
% 0.16/0.40 = ( ^ [X: A,Y5: B] : C3 ) ) ).
% 0.16/0.40
% 0.16/0.40 % curry_K
% 0.16/0.40 thf(fact_219_curryD,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,F: ( product_prod @ A @ B ) > $o,A2: A,B2: B] :
% 0.16/0.40 ( ( product_curry @ A @ B @ $o @ F @ A2 @ B2 )
% 0.16/0.40 => ( F @ ( product_Pair @ A @ B @ A2 @ B2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % curryD
% 0.16/0.40 thf(fact_220_curryE,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,F: ( product_prod @ A @ B ) > $o,A2: A,B2: B] :
% 0.16/0.40 ( ( product_curry @ A @ B @ $o @ F @ A2 @ B2 )
% 0.16/0.40 => ( F @ ( product_Pair @ A @ B @ A2 @ B2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % curryE
% 0.16/0.40 thf(fact_221_curry__def,axiom,
% 0.16/0.40 ! [C: $tType,B: $tType,A: $tType] :
% 0.16/0.40 ( ( product_curry @ A @ B @ C )
% 0.16/0.40 = ( ^ [C4: ( product_prod @ A @ B ) > C,X: A,Y5: B] : ( C4 @ ( product_Pair @ A @ B @ X @ Y5 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % curry_def
% 0.16/0.40 thf(fact_222_adm__lemma,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ A ),F8: ( A > B ) > A > B] :
% 0.16/0.40 ( adm_wf @ A @ B @ R
% 0.16/0.40 @ ^ [F7: A > B,X: A] : ( F8 @ ( cut @ A @ B @ F7 @ R @ X ) @ X ) ) ).
% 0.16/0.40
% 0.16/0.40 % adm_lemma
% 0.16/0.40 thf(fact_223_accp__acc__eq,axiom,
% 0.16/0.40 ! [A: $tType,R3: set @ ( product_prod @ A @ A )] :
% 0.16/0.40 ( ( accp @ A
% 0.16/0.40 @ ^ [X: A,Y5: A] : ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y5 ) @ R3 ) )
% 0.16/0.40 = ( ^ [X: A] : ( member @ A @ X @ ( acc @ A @ R3 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % accp_acc_eq
% 0.16/0.40 thf(fact_224_acc_Ocases,axiom,
% 0.16/0.40 ! [A: $tType,A2: A,R3: set @ ( product_prod @ A @ A )] :
% 0.16/0.40 ( ( member @ A @ A2 @ ( acc @ A @ R3 ) )
% 0.16/0.40 => ! [Y7: A] :
% 0.16/0.40 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y7 @ A2 ) @ R3 )
% 0.16/0.40 => ( member @ A @ Y7 @ ( acc @ A @ R3 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % acc.cases
% 0.16/0.40 thf(fact_225_acc_Osimps,axiom,
% 0.16/0.40 ! [A: $tType,A2: A,R3: set @ ( product_prod @ A @ A )] :
% 0.16/0.40 ( ( member @ A @ A2 @ ( acc @ A @ R3 ) )
% 0.16/0.40 = ( ? [X: A] :
% 0.16/0.40 ( ( A2 = X )
% 0.16/0.40 & ! [Y5: A] :
% 0.16/0.40 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y5 @ X ) @ R3 )
% 0.16/0.40 => ( member @ A @ Y5 @ ( acc @ A @ R3 ) ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % acc.simps
% 0.16/0.40 thf(fact_226_acc_Ointros,axiom,
% 0.16/0.40 ! [A: $tType,X7: A,R3: set @ ( product_prod @ A @ A )] :
% 0.16/0.40 ( ! [Y4: A] :
% 0.16/0.40 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y4 @ X7 ) @ R3 )
% 0.16/0.40 => ( member @ A @ Y4 @ ( acc @ A @ R3 ) ) )
% 0.16/0.40 => ( member @ A @ X7 @ ( acc @ A @ R3 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % acc.intros
% 0.16/0.40 thf(fact_227_acc__induct,axiom,
% 0.16/0.40 ! [A: $tType,A2: A,R3: set @ ( product_prod @ A @ A ),P3: A > $o] :
% 0.16/0.40 ( ( member @ A @ A2 @ ( acc @ A @ R3 ) )
% 0.16/0.40 => ( ! [X6: A] :
% 0.16/0.40 ( ( member @ A @ X6 @ ( acc @ A @ R3 ) )
% 0.16/0.40 => ( ! [Y7: A] :
% 0.16/0.40 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y7 @ X6 ) @ R3 )
% 0.16/0.40 => ( P3 @ Y7 ) )
% 0.16/0.40 => ( P3 @ X6 ) ) )
% 0.16/0.40 => ( P3 @ A2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % acc_induct
% 0.16/0.40 thf(fact_228_acc_Oinducts,axiom,
% 0.16/0.40 ! [A: $tType,X7: A,R3: set @ ( product_prod @ A @ A ),P3: A > $o] :
% 0.16/0.40 ( ( member @ A @ X7 @ ( acc @ A @ R3 ) )
% 0.16/0.40 => ( ! [X6: A] :
% 0.16/0.40 ( ! [Y7: A] :
% 0.16/0.40 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y7 @ X6 ) @ R3 )
% 0.16/0.40 => ( member @ A @ Y7 @ ( acc @ A @ R3 ) ) )
% 0.16/0.40 => ( ! [Y7: A] :
% 0.16/0.40 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y7 @ X6 ) @ R3 )
% 0.16/0.40 => ( P3 @ Y7 ) )
% 0.16/0.40 => ( P3 @ X6 ) ) )
% 0.16/0.40 => ( P3 @ X7 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % acc.inducts
% 0.16/0.40 thf(fact_229_acc__downward,axiom,
% 0.16/0.40 ! [A: $tType,B2: A,R3: set @ ( product_prod @ A @ A ),A2: A] :
% 0.16/0.40 ( ( member @ A @ B2 @ ( acc @ A @ R3 ) )
% 0.16/0.40 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ R3 )
% 0.16/0.40 => ( member @ A @ A2 @ ( acc @ A @ R3 ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % acc_downward
% 0.16/0.40 thf(fact_230_not__acc__down,axiom,
% 0.16/0.40 ! [A: $tType,X7: A,R: set @ ( product_prod @ A @ A )] :
% 0.16/0.40 ( ~ ( member @ A @ X7 @ ( acc @ A @ R ) )
% 0.16/0.40 => ~ ! [Z3: A] :
% 0.16/0.40 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Z3 @ X7 ) @ R )
% 0.16/0.40 => ( member @ A @ Z3 @ ( acc @ A @ R ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % not_acc_down
% 0.16/0.40 thf(fact_231_acc__induct__rule,axiom,
% 0.16/0.40 ! [A: $tType,A2: A,R3: set @ ( product_prod @ A @ A ),P3: A > $o] :
% 0.16/0.40 ( ( member @ A @ A2 @ ( acc @ A @ R3 ) )
% 0.16/0.40 => ( ! [X6: A] :
% 0.16/0.40 ( ( member @ A @ X6 @ ( acc @ A @ R3 ) )
% 0.16/0.40 => ( ! [Y7: A] :
% 0.16/0.40 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y7 @ X6 ) @ R3 )
% 0.16/0.40 => ( P3 @ Y7 ) )
% 0.16/0.40 => ( P3 @ X6 ) ) )
% 0.16/0.40 => ( P3 @ A2 ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % acc_induct_rule
% 0.16/0.40 thf(fact_232_adm__wf__def,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType] :
% 0.16/0.40 ( ( adm_wf @ A @ B )
% 0.16/0.40 = ( ^ [R2: set @ ( product_prod @ A @ A ),F9: ( A > B ) > A > B] :
% 0.16/0.40 ! [F7: A > B,G4: A > B,X: A] :
% 0.16/0.40 ( ! [Z4: A] :
% 0.16/0.40 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Z4 @ X ) @ R2 )
% 0.16/0.40 => ( ( F7 @ Z4 )
% 0.16/0.40 = ( G4 @ Z4 ) ) )
% 0.16/0.40 => ( ( F9 @ F7 @ X )
% 0.16/0.40 = ( F9 @ G4 @ X ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % adm_wf_def
% 0.16/0.40 thf(fact_233_acc__def,axiom,
% 0.16/0.40 ! [A: $tType] :
% 0.16/0.40 ( ( acc @ A )
% 0.16/0.40 = ( ^ [R4: set @ ( product_prod @ A @ A )] :
% 0.16/0.40 ( collect @ A
% 0.16/0.40 @ ( accp @ A
% 0.16/0.40 @ ^ [X: A,Y5: A] : ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y5 ) @ R4 ) ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 % acc_def
% 0.16/0.40 thf(fact_234_process__term_Octr__transfer_I2_J,axiom,
% 0.16/0.40 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o] : ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( proces749077512rocess @ A @ B @ R1 ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( proces1062592052s_PROC @ A @ Pvar ) @ ( proces1062592052s_PROC @ B @ C ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_term.ctr_transfer(2)
% 0.16/0.40 thf(fact_235_in__inv__image,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,X7: A,Y3: A,R3: set @ ( product_prod @ B @ B ),F: A > B] :
% 0.16/0.40 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X7 @ Y3 ) @ ( inv_image @ B @ A @ R3 @ F ) )
% 0.16/0.40 = ( member @ ( product_prod @ B @ B ) @ ( product_Pair @ B @ B @ ( F @ X7 ) @ ( F @ Y3 ) ) @ R3 ) ) ).
% 0.16/0.40
% 0.16/0.40 % in_inv_image
% 0.16/0.40 thf(fact_236_process__term_Octr__transfer_I1_J,axiom,
% 0.16/0.40 ! [Pvar: $tType,A: $tType,B: $tType,C: $tType,R22: Pvar > C > $o,R1: A > B > $o] : ( bNF_rel_fun @ Pvar @ C @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ R22 @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( proces1627516585ss_VAR @ Pvar @ A ) @ ( proces1627516585ss_VAR @ C @ B ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_term.ctr_transfer(1)
% 0.16/0.40 thf(fact_237_process__term_Orec__transfer,axiom,
% 0.16/0.40 ! [Pvar: $tType,D: $tType,A: $tType,B: $tType,E: $tType,C: $tType,R22: Pvar > C > $o,S: D > E > $o,R1: A > B > $o] : ( bNF_rel_fun @ ( Pvar > D ) @ ( C > E ) @ ( ( ( proces634752977rocess @ A ) > D ) > ( A > ( proces554692349s_term @ A @ Pvar ) > D > D ) > ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( ( proces634752977rocess @ B ) > E ) > ( B > ( proces554692349s_term @ B @ C ) > E > E ) > ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E > E > E ) > ( proces554692349s_term @ B @ C ) > E ) @ ( bNF_rel_fun @ Pvar @ C @ D @ E @ R22 @ S ) @ ( bNF_rel_fun @ ( ( proces634752977rocess @ A ) > D ) @ ( ( proces634752977rocess @ B ) > E ) @ ( ( A > ( proces554692349s_term @ A @ Pvar ) > D > D ) > ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( B > ( proces554692349s_term @ B @ C ) > E > E ) > ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E > E > E ) > ( proces554692349s_term @ B @ C ) > E ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ D @ E @ ( proces749077512rocess @ A @ B @ R1 ) @ S ) @ ( bNF_rel_fun @ ( A > ( proces554692349s_term @ A @ Pvar ) > D > D ) @ ( B > ( proces554692349s_term @ B @ C ) > E > E ) @ ( ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E > E > E ) > ( proces554692349s_term @ B @ C ) > E ) @ ( bNF_rel_fun @ A @ B @ ( ( proces554692349s_term @ A @ Pvar ) > D > D ) @ ( ( proces554692349s_term @ B @ C ) > E > E ) @ R1 @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( D > D ) @ ( E > E ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( bNF_rel_fun @ D @ E @ D @ E @ S @ S ) ) ) @ ( bNF_rel_fun @ ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D ) @ ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E > E > E ) @ ( ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( proces554692349s_term @ B @ C ) > E ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( ( proces554692349s_term @ A @ Pvar ) > D > D > D ) @ ( ( proces554692349s_term @ B @ C ) > E > E > E ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( D > D > D ) @ ( E > E > E ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( bNF_rel_fun @ D @ E @ ( D > D ) @ ( E > E ) @ S @ ( bNF_rel_fun @ D @ E @ D @ E @ S @ S ) ) ) ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ D @ E @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ S ) ) ) ) @ ( proces2117273769s_term @ Pvar @ D @ A ) @ ( proces2117273769s_term @ C @ E @ B ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_term.rec_transfer
% 0.16/0.40 thf(fact_238_process__term_Ocase__transfer,axiom,
% 0.16/0.40 ! [Pvar: $tType,D: $tType,A: $tType,B: $tType,E: $tType,C: $tType,R22: Pvar > C > $o,S: D > E > $o,R1: A > B > $o] : ( bNF_rel_fun @ ( Pvar > D ) @ ( C > E ) @ ( ( ( proces634752977rocess @ A ) > D ) > ( A > ( proces554692349s_term @ A @ Pvar ) > D ) > ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( ( proces634752977rocess @ B ) > E ) > ( B > ( proces554692349s_term @ B @ C ) > E ) > ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E ) > ( proces554692349s_term @ B @ C ) > E ) @ ( bNF_rel_fun @ Pvar @ C @ D @ E @ R22 @ S ) @ ( bNF_rel_fun @ ( ( proces634752977rocess @ A ) > D ) @ ( ( proces634752977rocess @ B ) > E ) @ ( ( A > ( proces554692349s_term @ A @ Pvar ) > D ) > ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( B > ( proces554692349s_term @ B @ C ) > E ) > ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E ) > ( proces554692349s_term @ B @ C ) > E ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ D @ E @ ( proces749077512rocess @ A @ B @ R1 ) @ S ) @ ( bNF_rel_fun @ ( A > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( B > ( proces554692349s_term @ B @ C ) > E ) @ ( ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E ) > ( proces554692349s_term @ B @ C ) > E ) @ ( bNF_rel_fun @ A @ B @ ( ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( proces554692349s_term @ B @ C ) > E ) @ R1 @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ D @ E @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ S ) ) @ ( bNF_rel_fun @ ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E ) @ ( ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( proces554692349s_term @ B @ C ) > E ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( proces554692349s_term @ B @ C ) > E ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ D @ E @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ S ) ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ D @ E @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ S ) ) ) ) @ ( proces460752237s_term @ Pvar @ D @ A ) @ ( proces460752237s_term @ C @ E @ B ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_term.case_transfer
% 0.16/0.40 thf(fact_239_process_Ocorec__transfer,axiom,
% 0.16/0.40 ! [C: $tType,A: $tType,B: $tType,D: $tType,S: C > D > $o,R: A > B > $o] :
% 0.16/0.40 ( bNF_rel_fun @ ( C > $o ) @ ( D > $o ) @ ( ( C > A ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > B ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) )
% 0.16/0.40 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ S
% 0.16/0.40 @ ^ [Y6: $o,Z: $o] : ( Y6 = Z ) )
% 0.16/0.40 @ ( bNF_rel_fun @ ( C > A ) @ ( D > B ) @ ( ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ A @ B @ S @ R )
% 0.16/0.40 @ ( bNF_rel_fun @ ( C > $o ) @ ( D > $o ) @ ( ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) )
% 0.16/0.40 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ S
% 0.16/0.40 @ ^ [Y6: $o,Z: $o] : ( Y6 = Z ) )
% 0.16/0.40 @ ( bNF_rel_fun @ ( C > ( proces634752977rocess @ A ) ) @ ( D > ( proces634752977rocess @ B ) ) @ ( ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ S @ ( proces749077512rocess @ A @ B @ R ) )
% 0.16/0.40 @ ( bNF_rel_fun @ ( C > C ) @ ( D > D ) @ ( ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ C @ D @ S @ S )
% 0.16/0.40 @ ( bNF_rel_fun @ ( C > $o ) @ ( D > $o ) @ ( ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) )
% 0.16/0.40 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ S
% 0.16/0.40 @ ^ [Y6: $o,Z: $o] : ( Y6 = Z ) )
% 0.16/0.40 @ ( bNF_rel_fun @ ( C > ( proces634752977rocess @ A ) ) @ ( D > ( proces634752977rocess @ B ) ) @ ( ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ S @ ( proces749077512rocess @ A @ B @ R ) )
% 0.16/0.40 @ ( bNF_rel_fun @ ( C > C ) @ ( D > D ) @ ( ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ C @ D @ S @ S )
% 0.16/0.40 @ ( bNF_rel_fun @ ( C > $o ) @ ( D > $o ) @ ( ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) )
% 0.16/0.40 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ S
% 0.16/0.40 @ ^ [Y6: $o,Z: $o] : ( Y6 = Z ) )
% 0.16/0.40 @ ( bNF_rel_fun @ ( C > ( proces634752977rocess @ A ) ) @ ( D > ( proces634752977rocess @ B ) ) @ ( ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > D ) > D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ S @ ( proces749077512rocess @ A @ B @ R ) ) @ ( bNF_rel_fun @ ( C > C ) @ ( D > D ) @ ( C > ( proces634752977rocess @ A ) ) @ ( D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ C @ D @ S @ S ) @ ( bNF_rel_fun @ C @ D @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ S @ ( proces749077512rocess @ A @ B @ R ) ) ) ) ) ) ) ) ) ) ) )
% 0.16/0.40 @ ( proces894737309rocess @ C @ A )
% 0.16/0.40 @ ( proces894737309rocess @ D @ B ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.corec_transfer
% 0.16/0.40 thf(fact_240_process_Odisc__transfer_I1_J,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,R: A > B > $o] :
% 0.16/0.40 ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ $o @ $o @ ( proces749077512rocess @ A @ B @ R )
% 0.16/0.40 @ ^ [Y6: $o,Z: $o] : ( Y6 = Z )
% 0.16/0.40 @ ( proces10484146Action @ A )
% 0.16/0.40 @ ( proces10484146Action @ B ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.disc_transfer(1)
% 0.16/0.40 thf(fact_241_process_Odisc__transfer_I2_J,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,R: A > B > $o] :
% 0.16/0.40 ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ $o @ $o @ ( proces749077512rocess @ A @ B @ R )
% 0.16/0.40 @ ^ [Y6: $o,Z: $o] : ( Y6 = Z )
% 0.16/0.40 @ ( proces401113213Choice @ A )
% 0.16/0.40 @ ( proces401113213Choice @ B ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.disc_transfer(2)
% 0.16/0.40 thf(fact_242_process_Octr__transfer_I2_J,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,R: A > B > $o] : ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) @ ( ( proces634752977rocess @ B ) > ( proces634752977rocess @ B ) ) @ ( proces749077512rocess @ A @ B @ R ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( proces749077512rocess @ A @ B @ R ) @ ( proces749077512rocess @ A @ B @ R ) ) @ ( proces1915862579Choice @ A ) @ ( proces1915862579Choice @ B ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.ctr_transfer(2)
% 0.16/0.40 thf(fact_243_process_Ocase__transfer,axiom,
% 0.16/0.40 ! [A: $tType,C: $tType,D: $tType,B: $tType,R: A > B > $o,S: C > D > $o] : ( bNF_rel_fun @ ( A > ( proces634752977rocess @ A ) > C ) @ ( B > ( proces634752977rocess @ B ) > D ) @ ( ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > C ) > ( proces634752977rocess @ A ) > C ) @ ( ( ( proces634752977rocess @ B ) > ( proces634752977rocess @ B ) > D ) > ( proces634752977rocess @ B ) > D ) @ ( bNF_rel_fun @ A @ B @ ( ( proces634752977rocess @ A ) > C ) @ ( ( proces634752977rocess @ B ) > D ) @ R @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ C @ D @ ( proces749077512rocess @ A @ B @ R ) @ S ) ) @ ( bNF_rel_fun @ ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > C ) @ ( ( proces634752977rocess @ B ) > ( proces634752977rocess @ B ) > D ) @ ( ( proces634752977rocess @ A ) > C ) @ ( ( proces634752977rocess @ B ) > D ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( ( proces634752977rocess @ A ) > C ) @ ( ( proces634752977rocess @ B ) > D ) @ ( proces749077512rocess @ A @ B @ R ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ C @ D @ ( proces749077512rocess @ A @ B @ R ) @ S ) ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ C @ D @ ( proces749077512rocess @ A @ B @ R ) @ S ) ) @ ( proces1406508781rocess @ A @ C ) @ ( proces1406508781rocess @ B @ D ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.case_transfer
% 0.16/0.40 thf(fact_244_process_Opred__transfer,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,R: A > B > $o] :
% 0.16/0.40 ( bNF_rel_fun @ ( A > $o ) @ ( B > $o ) @ ( ( proces634752977rocess @ A ) > $o ) @ ( ( proces634752977rocess @ B ) > $o )
% 0.16/0.40 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ R
% 0.16/0.40 @ ^ [Y6: $o,Z: $o] : ( Y6 = Z ) )
% 0.16/0.40 @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ $o @ $o @ ( proces749077512rocess @ A @ B @ R )
% 0.16/0.40 @ ^ [Y6: $o,Z: $o] : ( Y6 = Z ) )
% 0.16/0.40 @ ( proces1205983068rocess @ A )
% 0.16/0.40 @ ( proces1205983068rocess @ B ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.pred_transfer
% 0.16/0.40 thf(fact_245_process_Orel__transfer,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,D: $tType,C: $tType,Sa: A > C > $o,Sc: B > D > $o] :
% 0.16/0.40 ( bNF_rel_fun @ ( A > B > $o ) @ ( C > D > $o ) @ ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ B ) > $o ) @ ( ( proces634752977rocess @ C ) > ( proces634752977rocess @ D ) > $o )
% 0.16/0.40 @ ( bNF_rel_fun @ A @ C @ ( B > $o ) @ ( D > $o ) @ Sa
% 0.16/0.40 @ ( bNF_rel_fun @ B @ D @ $o @ $o @ Sc
% 0.16/0.40 @ ^ [Y6: $o,Z: $o] : ( Y6 = Z ) ) )
% 0.16/0.40 @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ C ) @ ( ( proces634752977rocess @ B ) > $o ) @ ( ( proces634752977rocess @ D ) > $o ) @ ( proces749077512rocess @ A @ C @ Sa )
% 0.16/0.40 @ ( bNF_rel_fun @ ( proces634752977rocess @ B ) @ ( proces634752977rocess @ D ) @ $o @ $o @ ( proces749077512rocess @ B @ D @ Sc )
% 0.16/0.40 @ ^ [Y6: $o,Z: $o] : ( Y6 = Z ) ) )
% 0.16/0.40 @ ( proces749077512rocess @ A @ B )
% 0.16/0.40 @ ( proces749077512rocess @ C @ D ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.rel_transfer
% 0.16/0.40 thf(fact_246_process_Octr__transfer_I1_J,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,R: A > B > $o] : ( bNF_rel_fun @ A @ B @ ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) @ ( ( proces634752977rocess @ B ) > ( proces634752977rocess @ B ) ) @ R @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( proces749077512rocess @ A @ B @ R ) @ ( proces749077512rocess @ A @ B @ R ) ) @ ( proces1525233512Action @ A ) @ ( proces1525233512Action @ B ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.ctr_transfer(1)
% 0.16/0.40 thf(fact_247_process__term_Octr__transfer_I4_J,axiom,
% 0.16/0.40 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o] : ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) ) @ ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) ) @ ( proces89589571ess_CH @ A @ Pvar ) @ ( proces89589571ess_CH @ B @ C ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_term.ctr_transfer(4)
% 0.16/0.40 thf(fact_248_process__term_Octr__transfer_I3_J,axiom,
% 0.16/0.40 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o] : ( bNF_rel_fun @ A @ B @ ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) ) @ ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) ) @ R1 @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) ) @ ( proces1454156180ss_ACT @ A @ Pvar ) @ ( proces1454156180ss_ACT @ B @ C ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_term.ctr_transfer(3)
% 0.16/0.40 thf(fact_249_process__term_Opred__transfer,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: B > D > $o] :
% 0.16/0.40 ( bNF_rel_fun @ ( A > $o ) @ ( C > $o ) @ ( ( B > $o ) > ( proces554692349s_term @ A @ B ) > $o ) @ ( ( D > $o ) > ( proces554692349s_term @ C @ D ) > $o )
% 0.16/0.40 @ ( bNF_rel_fun @ A @ C @ $o @ $o @ R1
% 0.16/0.40 @ ^ [Y6: $o,Z: $o] : ( Y6 = Z ) )
% 0.16/0.40 @ ( bNF_rel_fun @ ( B > $o ) @ ( D > $o ) @ ( ( proces554692349s_term @ A @ B ) > $o ) @ ( ( proces554692349s_term @ C @ D ) > $o )
% 0.16/0.40 @ ( bNF_rel_fun @ B @ D @ $o @ $o @ R22
% 0.16/0.40 @ ^ [Y6: $o,Z: $o] : ( Y6 = Z ) )
% 0.16/0.40 @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ B ) @ ( proces554692349s_term @ C @ D ) @ $o @ $o @ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 )
% 0.16/0.40 @ ^ [Y6: $o,Z: $o] : ( Y6 = Z ) ) )
% 0.16/0.40 @ ( proces2118920028s_term @ A @ B )
% 0.16/0.40 @ ( proces2118920028s_term @ C @ D ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_term.pred_transfer
% 0.16/0.40 thf(fact_250_process__term_Orel__transfer,axiom,
% 0.16/0.40 ! [A: $tType,C: $tType,B: $tType,D: $tType,H2: $tType,F5: $tType,G2: $tType,E: $tType,S1a: A > E > $o,S1c: C > G2 > $o,S2a: B > F5 > $o,S2c: D > H2 > $o] :
% 0.16/0.40 ( bNF_rel_fun @ ( A > C > $o ) @ ( E > G2 > $o ) @ ( ( B > D > $o ) > ( proces554692349s_term @ A @ B ) > ( proces554692349s_term @ C @ D ) > $o ) @ ( ( F5 > H2 > $o ) > ( proces554692349s_term @ E @ F5 ) > ( proces554692349s_term @ G2 @ H2 ) > $o )
% 0.16/0.40 @ ( bNF_rel_fun @ A @ E @ ( C > $o ) @ ( G2 > $o ) @ S1a
% 0.16/0.40 @ ( bNF_rel_fun @ C @ G2 @ $o @ $o @ S1c
% 0.16/0.40 @ ^ [Y6: $o,Z: $o] : ( Y6 = Z ) ) )
% 0.16/0.40 @ ( bNF_rel_fun @ ( B > D > $o ) @ ( F5 > H2 > $o ) @ ( ( proces554692349s_term @ A @ B ) > ( proces554692349s_term @ C @ D ) > $o ) @ ( ( proces554692349s_term @ E @ F5 ) > ( proces554692349s_term @ G2 @ H2 ) > $o )
% 0.16/0.40 @ ( bNF_rel_fun @ B @ F5 @ ( D > $o ) @ ( H2 > $o ) @ S2a
% 0.16/0.40 @ ( bNF_rel_fun @ D @ H2 @ $o @ $o @ S2c
% 0.16/0.40 @ ^ [Y6: $o,Z: $o] : ( Y6 = Z ) ) )
% 0.16/0.40 @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ B ) @ ( proces554692349s_term @ E @ F5 ) @ ( ( proces554692349s_term @ C @ D ) > $o ) @ ( ( proces554692349s_term @ G2 @ H2 ) > $o ) @ ( proces2029722208s_term @ A @ E @ B @ F5 @ S1a @ S2a )
% 0.16/0.40 @ ( bNF_rel_fun @ ( proces554692349s_term @ C @ D ) @ ( proces554692349s_term @ G2 @ H2 ) @ $o @ $o @ ( proces2029722208s_term @ C @ G2 @ D @ H2 @ S1c @ S2c )
% 0.16/0.40 @ ^ [Y6: $o,Z: $o] : ( Y6 = Z ) ) ) )
% 0.16/0.40 @ ( proces2029722208s_term @ A @ C @ B @ D )
% 0.16/0.40 @ ( proces2029722208s_term @ E @ G2 @ F5 @ H2 ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_term.rel_transfer
% 0.16/0.40 thf(fact_251_process__term_Omap__transfer,axiom,
% 0.16/0.40 ! [A: $tType,C: $tType,B: $tType,D: $tType,L: $tType,J: $tType,K: $tType,I: $tType,R1b: A > I > $o,S1d: C > K > $o,R2b: B > J > $o,S2d: D > L > $o] : ( bNF_rel_fun @ ( A > C ) @ ( I > K ) @ ( ( B > D ) > ( proces554692349s_term @ A @ B ) > ( proces554692349s_term @ C @ D ) ) @ ( ( J > L ) > ( proces554692349s_term @ I @ J ) > ( proces554692349s_term @ K @ L ) ) @ ( bNF_rel_fun @ A @ I @ C @ K @ R1b @ S1d ) @ ( bNF_rel_fun @ ( B > D ) @ ( J > L ) @ ( ( proces554692349s_term @ A @ B ) > ( proces554692349s_term @ C @ D ) ) @ ( ( proces554692349s_term @ I @ J ) > ( proces554692349s_term @ K @ L ) ) @ ( bNF_rel_fun @ B @ J @ D @ L @ R2b @ S2d ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ B ) @ ( proces554692349s_term @ I @ J ) @ ( proces554692349s_term @ C @ D ) @ ( proces554692349s_term @ K @ L ) @ ( proces2029722208s_term @ A @ I @ B @ J @ R1b @ R2b ) @ ( proces2029722208s_term @ C @ K @ D @ L @ S1d @ S2d ) ) ) @ ( proces224683037s_term @ A @ C @ B @ D ) @ ( proces224683037s_term @ I @ K @ J @ L ) ) ).
% 0.16/0.40
% 0.16/0.40 % process_term.map_transfer
% 0.16/0.40 thf(fact_252_process_Omap__transfer,axiom,
% 0.16/0.40 ! [A: $tType,B: $tType,F5: $tType,E: $tType,Rb: A > E > $o,Sd: B > F5 > $o] : ( bNF_rel_fun @ ( A > B ) @ ( E > F5 ) @ ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ B ) ) @ ( ( proces634752977rocess @ E ) > ( proces634752977rocess @ F5 ) ) @ ( bNF_rel_fun @ A @ E @ B @ F5 @ Rb @ Sd ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ E ) @ ( proces634752977rocess @ B ) @ ( proces634752977rocess @ F5 ) @ ( proces749077512rocess @ A @ E @ Rb ) @ ( proces749077512rocess @ B @ F5 @ Sd ) ) @ ( proces370407749rocess @ A @ B ) @ ( proces370407749rocess @ E @ F5 ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.map_transfer
% 0.16/0.40 thf(fact_253_process_Omap__disc__iff_I1_J,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,F: A > B,A2: proces634752977rocess @ A] :
% 0.16/0.40 ( ( proces10484146Action @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
% 0.16/0.40 = ( proces10484146Action @ A @ A2 ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.map_disc_iff(1)
% 0.16/0.40 thf(fact_254_process_Omap__disc__iff_I2_J,axiom,
% 0.16/0.40 ! [B: $tType,A: $tType,F: A > B,A2: proces634752977rocess @ A] :
% 0.16/0.40 ( ( proces401113213Choice @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
% 0.16/0.40 = ( proces401113213Choice @ A @ A2 ) ) ).
% 0.16/0.40
% 0.16/0.40 % process.map_disc_iff(2)
% 0.16/0.40
% 0.16/0.40 %----Helper facts (3)
% 0.16/0.40 thf(help_If_3_1_T,axiom,
% 0.16/0.40 ! [P3: $o] :
% 0.16/0.40 ( ( P3 = $true )
% 0.16/0.40 | ( P3 = $false ) ) ).
% 0.16/0.40
% 0.16/0.40 thf(help_If_2_1_T,axiom,
% 0.16/0.40 ! [A: $tType,X7: A,Y3: A] :
% 0.16/0.40 ( ( if @ A @ $false @ X7 @ Y3 )
% 0.16/0.40 = Y3 ) ).
% 0.16/0.40
% 0.16/0.40 thf(help_If_1_1_T,axiom,
% 0.16/0.40 ! [A: $tType,X7: A,Y3: A] :
% 0.16/0.40 ( ( if @ A @ $true @ X7 @ Y3 )
% 0.16/0.40 = X7 ) ).
% 0.16/0.40
% 0.16/0.40 %----Conjectures (1)
% 0.16/0.40 thf(conj_0,conjecture,
% 0.16/0.40 ( ( a3 = a2 )
% 0.16/0.40 & ( p2
% 0.16/0.40 = ( proces1652378886lution @ b @ a @ sys @ ( proces1062592052s_PROC @ a @ b @ pa ) ) ) ) ).
% 0.16/0.40
% 0.16/0.40 %------------------------------------------------------------------------------
% 0.16/0.40 ------------------------
% 3.45/1.75 ---- Embedded in THF ---
% 3.45/1.76 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.45/1.76 %%% Generated on Tue Feb 24 11:29:44 EST 2026
% 3.45/1.76 %%% using '$$dhol' embedding, version 1.3.0.
% 3.45/1.76 %%% Logic specification used:
% 3.45/1.76 %%% thf(spec, logic, $$dhol).
% 3.45/1.76
% 3.45/1.76 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.sFYK9PDrEK/DTF2DTF15624.p
% 3.45/1.76 thf(ty_t_Process__Mirabelle__xovoopgpgi_Oprocess__term, type, proces554692349s_term: ($tType > ($tType > $tType))).
% 3.45/1.76 thf(ty_t_Process__Mirabelle__xovoopgpgi_Oprocess, type, proces634752977rocess: ($tType > $tType)).
% 3.45/1.76 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 3.45/1.76 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 3.45/1.76 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 3.45/1.76 thf(ty_tf_b, type, b: $tType).
% 3.45/1.76 thf(ty_tf_a, type, a: $tType).
% 3.45/1.76 thf(sy_c_BNF__Def_Orel__fun, type, bNF_rel_fun: (!> [A:$tType,C:$tType,B:$tType,D:$tType]: (((A > (C > $o)) > ((B > (D > $o)) > ((A > B) > ((C > D) > $o))))))).
% 3.45/1.76 thf(sy_c_HOL_Oundefined, type, undefined: (!> [A:$tType]: (A))).
% 3.45/1.76 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 3.45/1.76 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH1, type, proces1239275103le_CH1: (!> [A:$tType,B:$tType]: (((A > ((proces554692349s_term @ B) @ A)) > (((proces554692349s_term @ B) @ A) > ((proces554692349s_term @ B) @ A)))))).
% 3.45/1.76 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH1__rel, type, proces1869379930H1_rel: (!> [A:$tType,B:$tType]: ((((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) > (((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) > $o))))).
% 3.45/1.76 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH2, type, proces1239275104le_CH2: (!> [A:$tType,B:$tType]: (((A > ((proces554692349s_term @ B) @ A)) > (((proces554692349s_term @ B) @ A) > ((proces554692349s_term @ B) @ A)))))).
% 3.45/1.76 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH2__rel, type, proces93903513H2_rel: (!> [A:$tType,B:$tType]: ((((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) > (((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) > $o))))).
% 3.45/1.76 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCONT, type, proces126235999e_CONT: (!> [A:$tType,B:$tType]: (((A > ((proces554692349s_term @ B) @ A)) > (((proces554692349s_term @ B) @ A) > ((proces554692349s_term @ B) @ A)))))).
% 3.45/1.76 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCONT__rel, type, proces1004198490NT_rel: (!> [A:$tType,B:$tType]: ((((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) > (((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) > $o))))).
% 3.45/1.76 thf(sy_c_Process__Mirabelle__xovoopgpgi_OPREF, type, proces1708129104e_PREF: (!> [A:$tType,B:$tType,C:$tType]: (((A > ((proces554692349s_term @ B) @ C)) > (((proces554692349s_term @ B) @ A) > B))))).
% 3.45/1.76 thf(sy_c_Process__Mirabelle__xovoopgpgi_OPREF__rel, type, proces527360425EF_rel: (!> [A:$tType,B:$tType,C:$tType]: ((((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A)) > (((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A)) > $o))))).
% 3.45/1.76 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oguarded, type, proces1121166967uarded: (!> [A:$tType,B:$tType,C:$tType]: (((A > ((proces554692349s_term @ B) @ C)) > $o)))).
% 3.45/1.76 thf(sy_c_Process__Mirabelle__xovoopgpgi_OisACT, type, proces687458811_isACT: (!> [A:$tType,B:$tType,C:$tType,D:$tType]: (((A > ((proces554692349s_term @ B) @ C)) > (((proces554692349s_term @ D) @ A) > $o))))).
% 3.45/1.76 thf(sy_c_Process__Mirabelle__xovoopgpgi_OisACT__rel, type, proces896239806CT_rel: (!> [A:$tType,B:$tType,C:$tType,D:$tType]: ((((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) > (((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) > $o))))).
% 3.45/1.76 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OAction, type, proces1525233512Action: (!> [A:$tType]: ((A > ((proces634752977rocess @ A) > (proces634752977rocess @ A)))))).
% 3.45/1.76 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OChoice, type, proces1915862579Choice: (!> [A:$tType]: (((proces634752977rocess @ A) > ((proces634752977rocess @ A) > (proces634752977rocess @ A)))))).
% 3.45/1.76 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Ocase__process, type, proces1406508781rocess: (!> [A:$tType,B:$tType]: (((A > ((proces634752977rocess @ A) > B)) > (((proces634752977rocess @ A) > ((proces634752977rocess @ A) > B)) > ((proces634752977rocess @ A) > B)))))).
% 3.45/1.76 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Och1Of, type, proces979765041_ch1Of: (!> [A:$tType]: (((proces634752977rocess @ A) > (proces634752977rocess @ A))))).
% 3.45/1.76 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Och2Of, type, proces988026546_ch2Of: (!> [A:$tType]: (((proces634752977rocess @ A) > (proces634752977rocess @ A))))).
% 3.45/1.76 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OcontOf, type, proces1778668539contOf: (!> [A:$tType]: (((proces634752977rocess @ A) > (proces634752977rocess @ A))))).
% 3.45/1.76 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Ocorec__process, type, proces894737309rocess: (!> [C:$tType,A:$tType]: (((C > $o) > ((C > A) > ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > (C > (proces634752977rocess @ A)))))))))))))))).
% 3.45/1.76 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OisAction, type, proces10484146Action: (!> [A:$tType]: (((proces634752977rocess @ A) > $o)))).
% 3.45/1.76 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OisChoice, type, proces401113213Choice: (!> [A:$tType]: (((proces634752977rocess @ A) > $o)))).
% 3.45/1.76 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Omap__process, type, proces370407749rocess: (!> [A:$tType,Aa:$tType]: (((A > Aa) > ((proces634752977rocess @ A) > (proces634752977rocess @ Aa)))))).
% 3.45/1.76 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Opred__process, type, proces1205983068rocess: (!> [A:$tType]: (((A > $o) > ((proces634752977rocess @ A) > $o))))).
% 3.45/1.76 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OprefOf, type, proces745025900prefOf: (!> [A:$tType]: (((proces634752977rocess @ A) > A)))).
% 3.45/1.76 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Orel__process, type, proces749077512rocess: (!> [A:$tType,B:$tType]: (((A > (B > $o)) > ((proces634752977rocess @ A) > ((proces634752977rocess @ B) > $o)))))).
% 3.45/1.76 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OACT, type, proces1454156180ss_ACT: (!> [A:$tType,Pvar:$tType]: ((A > (((proces554692349s_term @ A) @ Pvar) > ((proces554692349s_term @ A) @ Pvar)))))).
% 3.45/1.76 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OCH, type, proces89589571ess_CH: (!> [A:$tType,Pvar:$tType]: ((((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > ((proces554692349s_term @ A) @ Pvar)))))).
% 3.45/1.76 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OPROC, type, proces1062592052s_PROC: (!> [A:$tType,Pvar:$tType]: (((proces634752977rocess @ A) > ((proces554692349s_term @ A) @ Pvar))))).
% 3.45/1.76 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OVAR, type, proces1627516585ss_VAR: (!> [Pvar:$tType,A:$tType]: ((Pvar > ((proces554692349s_term @ A) @ Pvar))))).
% 3.45/1.76 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Ocase__process__term, type, proces460752237s_term: (!> [Pvar:$tType,B:$tType,A:$tType]: (((Pvar > B) > (((proces634752977rocess @ A) > B) > ((A > (((proces554692349s_term @ A) @ Pvar) > B)) > ((((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > B)) > (((proces554692349s_term @ A) @ Pvar) > B)))))))).
% 3.45/1.76 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Omap__process__term, type, proces224683037s_term: (!> [A:$tType,Aa:$tType,Pvar:$tType,Pvara:$tType]: (((A > Aa) > ((Pvar > Pvara) > (((proces554692349s_term @ A) @ Pvar) > ((proces554692349s_term @ Aa) @ Pvara))))))).
% 3.45/1.76 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Opred__process__term, type, proces2118920028s_term: (!> [A:$tType,B:$tType]: (((A > $o) > ((B > $o) > (((proces554692349s_term @ A) @ B) > $o)))))).
% 3.45/1.76 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Orec__process__term, type, proces2117273769s_term: (!> [Pvar:$tType,D:$tType,A:$tType]: (((Pvar > D) > (((proces634752977rocess @ A) > D) > ((A > (((proces554692349s_term @ A) @ Pvar) > (D > D))) > ((((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > (D > (D > D)))) > (((proces554692349s_term @ A) @ Pvar) > D)))))))).
% 3.45/1.76 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Orel__process__term, type, proces2029722208s_term: (!> [A:$tType,C:$tType,B:$tType,D:$tType]: (((A > (C > $o)) > ((B > (D > $o)) > (((proces554692349s_term @ A) @ B) > (((proces554692349s_term @ C) @ D) > $o))))))).
% 3.45/1.76 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Oset2__process__term, type, proces1493547885s_term: (!> [A:$tType,Pvar:$tType]: ((((proces554692349s_term @ A) @ Pvar) > (set @ Pvar))))).
% 3.45/1.76 thf(sy_c_Process__Mirabelle__xovoopgpgi_Osolution, type, proces1652378886lution: (!> [A:$tType,B:$tType]: (((A > ((proces554692349s_term @ B) @ A)) > (((proces554692349s_term @ B) @ A) > (proces634752977rocess @ B)))))).
% 3.45/1.76 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 3.45/1.76 thf(sy_c_Product__Type_Ocurry, type, product_curry: (!> [A:$tType,B:$tType,C:$tType]: (((((product_prod @ A) @ B) > C) > (A > (B > C)))))).
% 3.45/1.76 thf(sy_c_Product__Type_Ointernal__case__prod, type, produc2004651681e_prod: (!> [A:$tType,B:$tType,C:$tType]: (((A > (B > C)) > (((product_prod @ A) @ B) > C))))).
% 3.45/1.76 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod, type, product_rec_prod: (!> [A:$tType,B:$tType,T:$tType]: (((A > (B > T)) > (((product_prod @ A) @ B) > T))))).
% 3.45/1.76 thf(sy_c_Pure_Otype, type, type: (!> [A:$tType]: ((itself @ A)))).
% 3.45/1.76 thf(sy_c_Relation_Oinv__image, type, inv_image: (!> [B:$tType,A:$tType]: (((set @ ((product_prod @ B) @ B)) > ((A > B) > (set @ ((product_prod @ A) @ A))))))).
% 3.45/1.76 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 3.45/1.76 thf(sy_c_Wellfounded_Oacc, type, acc: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > (set @ A))))).
% 3.45/1.76 thf(sy_c_Wellfounded_Oaccp, type, accp: (!> [A:$tType]: (((A > (A > $o)) > (A > $o))))).
% 3.45/1.76 thf(sy_c_Wellfounded_Olex__prod, type, lex_prod: (!> [A:$tType,B:$tType]: (((set @ ((product_prod @ A) @ A)) > ((set @ ((product_prod @ B) @ B)) > (set @ ((product_prod @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B)))))))).
% 3.45/1.76 thf(sy_c_Wfrec_Oadm__wf, type, adm_wf: (!> [A:$tType,B:$tType]: (((set @ ((product_prod @ A) @ A)) > (((A > B) > (A > B)) > $o))))).
% 3.45/1.76 thf(sy_c_Wfrec_Ocut, type, cut: (!> [A:$tType,B:$tType]: (((A > B) > ((set @ ((product_prod @ A) @ A)) > (A > (A > B))))))).
% 3.45/1.76 thf(sy_c_Wfrec_Osame__fst, type, same_fst: (!> [A:$tType,B:$tType]: (((A > $o) > ((A > (set @ ((product_prod @ B) @ B))) > (set @ ((product_prod @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B)))))))).
% 3.45/1.76 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 3.45/1.76 thf(sy_v_a_H____, type, a2: a).
% 3.45/1.76 thf(sy_v_a____, type, a3: a).
% 3.45/1.76 thf(sy_v_p, type, p: (proces634752977rocess @ a)).
% 3.45/1.76 thf(sy_v_p_H____, type, p2: (proces634752977rocess @ a)).
% 3.45/1.76 thf(sy_v_pa____, type, pa: (proces634752977rocess @ a)).
% 3.45/1.76 thf(sy_v_q____, type, q: (proces634752977rocess @ a)).
% 3.45/1.76 thf(sy_v_sys, type, sys: (b > ((proces554692349s_term @ a) @ b))).
% 3.45/1.76 thf(fact_0__092_060open_062q_A_061_Asolution_Asys_A_IPROC_Ap_J_092_060close_062, axiom, (q = ((((proces1652378886lution @ b) @ a) @ sys) @ (((proces1062592052s_PROC @ a) @ b) @ p)))).
% 3.45/1.76 thf(fact_1_process__term_Oinject_I2_J, axiom, (! [Pvar:$tType,A:$tType,X2:(proces634752977rocess @ A),Y2:(proces634752977rocess @ A)]: ((((((proces1062592052s_PROC @ A) @ Pvar) @ X2) = (((proces1062592052s_PROC @ A) @ Pvar) @ Y2)) = (X2 = Y2))))).
% 3.45/1.76 thf(fact_2_Action, axiom, ((((proces1525233512Action @ a) @ a2) @ p2) = ((((proces1652378886lution @ b) @ a) @ sys) @ (((proces1062592052s_PROC @ a) @ b) @ (((proces1525233512Action @ a) @ a3) @ pa))))).
% 3.45/1.76 thf(fact_3__C0_C, axiom, ((((((proces687458811_isACT @ b) @ a) @ b) @ a) @ sys) @ (((proces1062592052s_PROC @ a) @ b) @ (((proces1525233512Action @ a) @ a3) @ pa)))).
% 3.45/1.76 thf(fact_4__092_060open_062solution_Asys_A_IPROC_A_IAction_Aa_Ap_J_J_A_061_AAction_A_IPREF_Asys_A_IPROC_A_IAction_Aa_Ap_J_J_J_A_Isolution_Asys_A_ICONT_Asys_A_IPROC_A_IAction_Aa_Ap_J_J_J_J_092_060close_062, axiom, (((((proces1652378886lution @ b) @ a) @ sys) @ (((proces1062592052s_PROC @ a) @ b) @ (((proces1525233512Action @ a) @ a3) @ pa))) = (((proces1525233512Action @ a) @ (((((proces1708129104e_PREF @ b) @ a) @ b) @ sys) @ (((proces1062592052s_PROC @ a) @ b) @ (((proces1525233512Action @ a) @ a3) @ pa)))) @ ((((proces1652378886lution @ b) @ a) @ sys) @ ((((proces126235999e_CONT @ b) @ a) @ sys) @ (((proces1062592052s_PROC @ a) @ b) @ (((proces1525233512Action @ a) @ a3) @ pa))))))).
% 3.45/1.76 thf(fact_5_process__term_Osimps_I22_J, axiom, (! [Pvar:$tType,D:$tType,A:$tType,F1:(Pvar > D),F2:((proces634752977rocess @ A) > D),F3:(A > (((proces554692349s_term @ A) @ Pvar) > (D > D))),F4:(((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > (D > (D > D)))),X2:(proces634752977rocess @ A)]: ((((((((((proces2117273769s_term @ Pvar) @ D) @ A) @ F1) @ F2) @ F3) @ F4) @ (((proces1062592052s_PROC @ A) @ Pvar) @ X2)) = (F2 @ X2))))).
% 3.45/1.76 thf(fact_6_process__term_Osimps_I18_J, axiom, (! [Pvar:$tType,B:$tType,A:$tType,F1:(Pvar > B),F2:((proces634752977rocess @ A) > B),F3:(A > (((proces554692349s_term @ A) @ Pvar) > B)),F4:(((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > B)),X2:(proces634752977rocess @ A)]: ((((((((((proces460752237s_term @ Pvar) @ B) @ A) @ F1) @ F2) @ F3) @ F4) @ (((proces1062592052s_PROC @ A) @ Pvar) @ X2)) = (F2 @ X2))))).
% 3.45/1.76 thf(fact_7_process__term_Odistinct_I7_J, axiom, (! [Pvar:$tType,A:$tType,X2:(proces634752977rocess @ A),X31:A,X32:((proces554692349s_term @ A) @ Pvar)]: (((((proces1062592052s_PROC @ A) @ Pvar) @ X2) != ((((proces1454156180ss_ACT @ A) @ Pvar) @ X31) @ X32))))).
% 3.45/1.76 thf(fact_8_process__term_Odistinct_I9_J, axiom, (! [Pvar:$tType,A:$tType,X2:(proces634752977rocess @ A),X41:((proces554692349s_term @ A) @ Pvar),X42:((proces554692349s_term @ A) @ Pvar)]: (((((proces1062592052s_PROC @ A) @ Pvar) @ X2) != ((((proces89589571ess_CH @ A) @ Pvar) @ X41) @ X42))))).
% 3.45/1.76 thf(fact_9_process__term_Odistinct_I1_J, axiom, (! [Pvar:$tType,A:$tType,X1:Pvar,X2:(proces634752977rocess @ A)]: (((((proces1627516585ss_VAR @ Pvar) @ A) @ X1) != (((proces1062592052s_PROC @ A) @ Pvar) @ X2))))).
% 3.45/1.76 thf(fact_10_process_Ocase__distrib, axiom, (! [B:$tType,C:$tType,A:$tType,H:(B > C),F1:(A > ((proces634752977rocess @ A) > B)),F2:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > B)),Process:(proces634752977rocess @ A)]: (((H @ (((((proces1406508781rocess @ A) @ B) @ F1) @ F2) @ Process)) = (((((proces1406508781rocess @ A) @ C) @ (^ [X12:A,X22:(proces634752977rocess @ A)]: ((H @ ((F1 @ X12) @ X22))))) @ (^ [X12:(proces634752977rocess @ A),X22:(proces634752977rocess @ A)]: ((H @ ((F2 @ X12) @ X22))))) @ Process))))).
% 3.45/1.76 thf(fact_11_process__term_Ocase__distrib, axiom, (! [B:$tType,C:$tType,Pvar:$tType,A:$tType,H:(B > C),F1:(Pvar > B),F2:((proces634752977rocess @ A) > B),F3:(A > (((proces554692349s_term @ A) @ Pvar) > B)),F4:(((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > B)),Process_term:((proces554692349s_term @ A) @ Pvar)]: (((H @ ((((((((proces460752237s_term @ Pvar) @ B) @ A) @ F1) @ F2) @ F3) @ F4) @ Process_term)) = ((((((((proces460752237s_term @ Pvar) @ C) @ A) @ (^ [X:Pvar]: ((H @ (F1 @ X))))) @ (^ [X:(proces634752977rocess @ A)]: ((H @ (F2 @ X))))) @ (^ [X12:A,X22:((proces554692349s_term @ A) @ Pvar)]: ((H @ ((F3 @ X12) @ X22))))) @ (^ [X12:((proces554692349s_term @ A) @ Pvar),X22:((proces554692349s_term @ A) @ Pvar)]: ((H @ ((F4 @ X12) @ X22))))) @ Process_term))))).
% 3.45/1.76 thf(fact_12_solution__VAR, axiom, (! [B:$tType,A:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),X3:A]: ((((((proces1121166967uarded @ A) @ B) @ A) @ Sys) => (((((proces1652378886lution @ A) @ B) @ Sys) @ (((proces1627516585ss_VAR @ A) @ B) @ X3)) = ((((proces1652378886lution @ A) @ B) @ Sys) @ (Sys @ X3))))))).
% 3.45/1.76 thf(fact_13_PREF_Osimps_I2_J, axiom, (! [A:$tType,C:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ C)),P:(proces634752977rocess @ B)]: (((((((proces1708129104e_PREF @ A) @ B) @ C) @ Sys) @ (((proces1062592052s_PROC @ B) @ A) @ P)) = ((proces745025900prefOf @ B) @ P))))).
% 3.45/1.76 thf(fact_14_process__term_Opred__inject_I2_J, axiom, (! [Pvar:$tType,A:$tType,P1:(A > $o),P2:(Pvar > $o),A2:(proces634752977rocess @ A)]: (((((((proces2118920028s_term @ A) @ Pvar) @ P1) @ P2) @ (((proces1062592052s_PROC @ A) @ Pvar) @ A2)) = (((proces1205983068rocess @ A) @ P1) @ A2))))).
% 3.45/1.76 thf(fact_15_process__term_Oinject_I1_J, axiom, (! [A:$tType,Pvar:$tType,X1:Pvar,Y1:Pvar]: ((((((proces1627516585ss_VAR @ Pvar) @ A) @ X1) = (((proces1627516585ss_VAR @ Pvar) @ A) @ Y1)) = (X1 = Y1))))).
% 3.45/1.76 thf(fact_16_process__term_Oinject_I4_J, axiom, (! [Pvar:$tType,A:$tType,X41:((proces554692349s_term @ A) @ Pvar),X42:((proces554692349s_term @ A) @ Pvar),Y41:((proces554692349s_term @ A) @ Pvar),Y42:((proces554692349s_term @ A) @ Pvar)]: (((((((proces89589571ess_CH @ A) @ Pvar) @ X41) @ X42) = ((((proces89589571ess_CH @ A) @ Pvar) @ Y41) @ Y42)) = ((X41 = Y41) & (X42 = Y42)))))).
% 3.45/1.76 thf(fact_17_process__term_Oinject_I3_J, axiom, (! [Pvar:$tType,A:$tType,X31:A,X32:((proces554692349s_term @ A) @ Pvar),Y31:A,Y32:((proces554692349s_term @ A) @ Pvar)]: (((((((proces1454156180ss_ACT @ A) @ Pvar) @ X31) @ X32) = ((((proces1454156180ss_ACT @ A) @ Pvar) @ Y31) @ Y32)) = ((X31 = Y31) & (X32 = Y32)))))).
% 3.45/1.76 thf(fact_18_process_Oinject_I1_J, axiom, (! [A:$tType,X11:A,X122:(proces634752977rocess @ A),Y11:A,Y12:(proces634752977rocess @ A)]: ((((((proces1525233512Action @ A) @ X11) @ X122) = (((proces1525233512Action @ A) @ Y11) @ Y12)) = ((X11 = Y11) & (X122 = Y12)))))).
% 3.45/1.76 thf(fact_19_process__term_Opred__inject_I1_J, axiom, (! [A:$tType,Pvar:$tType,P1:(A > $o),P2:(Pvar > $o),A2:Pvar]: (((((((proces2118920028s_term @ A) @ Pvar) @ P1) @ P2) @ (((proces1627516585ss_VAR @ Pvar) @ A) @ A2)) = (P2 @ A2))))).
% 3.45/1.76 thf(fact_20_process__term_Opred__inject_I4_J, axiom, (! [Pvar:$tType,A:$tType,P1:(A > $o),P2:(Pvar > $o),A2:((proces554692349s_term @ A) @ Pvar),Aa2:((proces554692349s_term @ A) @ Pvar)]: (((((((proces2118920028s_term @ A) @ Pvar) @ P1) @ P2) @ ((((proces89589571ess_CH @ A) @ Pvar) @ A2) @ Aa2)) = ((((((proces2118920028s_term @ A) @ Pvar) @ P1) @ P2) @ A2) & (((((proces2118920028s_term @ A) @ Pvar) @ P1) @ P2) @ Aa2)))))).
% 3.45/1.76 thf(fact_21_process__term_Opred__inject_I3_J, axiom, (! [Pvar:$tType,A:$tType,P1:(A > $o),P2:(Pvar > $o),A2:A,Aa2:((proces554692349s_term @ A) @ Pvar)]: (((((((proces2118920028s_term @ A) @ Pvar) @ P1) @ P2) @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ A2) @ Aa2)) = ((P1 @ A2) & (((((proces2118920028s_term @ A) @ Pvar) @ P1) @ P2) @ Aa2)))))).
% 3.45/1.76 thf(fact_22_process_Opred__inject_I1_J, axiom, (! [A:$tType,P3:(A > $o),A2:A,Aa2:(proces634752977rocess @ A)]: (((((proces1205983068rocess @ A) @ P3) @ (((proces1525233512Action @ A) @ A2) @ Aa2)) = ((P3 @ A2) & (((proces1205983068rocess @ A) @ P3) @ Aa2)))))).
% 3.45/1.76 thf(fact_23_CONT_Osimps_I3_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),A2:B,T2:((proces554692349s_term @ B) @ A)]: ((((((proces126235999e_CONT @ A) @ B) @ Sys) @ ((((proces1454156180ss_ACT @ B) @ A) @ A2) @ T2)) = T2)))).
% 3.45/1.76 thf(fact_24_PREF_Osimps_I3_J, axiom, (! [A:$tType,C:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ C)),A2:B,T2:((proces554692349s_term @ B) @ A)]: (((((((proces1708129104e_PREF @ A) @ B) @ C) @ Sys) @ ((((proces1454156180ss_ACT @ B) @ A) @ A2) @ T2)) = A2)))).
% 3.45/1.76 thf(fact_25_isACT_Osimps_I4_J, axiom, (! [B:$tType,C:$tType,A:$tType,D:$tType,Sys:(A > ((proces554692349s_term @ B) @ C)),T1:((proces554692349s_term @ D) @ A),T22:((proces554692349s_term @ D) @ A)]: ((~ (((((((proces687458811_isACT @ A) @ B) @ C) @ D) @ Sys) @ ((((proces89589571ess_CH @ D) @ A) @ T1) @ T22))))))).
% 3.45/1.76 thf(fact_26_isACT_Osimps_I3_J, axiom, (! [B:$tType,C:$tType,A:$tType,D:$tType,Sys:(A > ((proces554692349s_term @ B) @ C)),A2:D,T2:((proces554692349s_term @ D) @ A)]: (((((((proces687458811_isACT @ A) @ B) @ C) @ D) @ Sys) @ ((((proces1454156180ss_ACT @ D) @ A) @ A2) @ T2))))).
% 3.45/1.76 thf(fact_27_process_Osel_I1_J, axiom, (! [A:$tType,X11:A,X122:(proces634752977rocess @ A)]: ((((proces745025900prefOf @ A) @ (((proces1525233512Action @ A) @ X11) @ X122)) = X11)))).
% 3.45/1.76 thf(fact_28_solution_Octr_I1_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T2:((proces554692349s_term @ B) @ A)]: ((((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ T2) => (((((proces1652378886lution @ A) @ B) @ Sys) @ T2) = (((proces1525233512Action @ B) @ (((((proces1708129104e_PREF @ A) @ B) @ A) @ Sys) @ T2)) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ ((((proces126235999e_CONT @ A) @ B) @ Sys) @ T2)))))))).
% 3.45/1.76 thf(fact_29_process_Osimps_I5_J, axiom, (! [B:$tType,A:$tType,F1:(A > ((proces634752977rocess @ A) > B)),F2:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > B)),X11:A,X122:(proces634752977rocess @ A)]: (((((((proces1406508781rocess @ A) @ B) @ F1) @ F2) @ (((proces1525233512Action @ A) @ X11) @ X122)) = ((F1 @ X11) @ X122))))).
% 3.45/1.76 thf(fact_30_process__term_Osimps_I24_J, axiom, (! [D:$tType,Pvar:$tType,A:$tType,F1:(Pvar > D),F2:((proces634752977rocess @ A) > D),F3:(A > (((proces554692349s_term @ A) @ Pvar) > (D > D))),F4:(((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > (D > (D > D)))),X41:((proces554692349s_term @ A) @ Pvar),X42:((proces554692349s_term @ A) @ Pvar)]: ((((((((((proces2117273769s_term @ Pvar) @ D) @ A) @ F1) @ F2) @ F3) @ F4) @ ((((proces89589571ess_CH @ A) @ Pvar) @ X41) @ X42)) = ((((F4 @ X41) @ X42) @ ((((((((proces2117273769s_term @ Pvar) @ D) @ A) @ F1) @ F2) @ F3) @ F4) @ X41)) @ ((((((((proces2117273769s_term @ Pvar) @ D) @ A) @ F1) @ F2) @ F3) @ F4) @ X42)))))).
% 3.45/1.76 thf(fact_31_process__term_Osimps_I23_J, axiom, (! [D:$tType,Pvar:$tType,A:$tType,F1:(Pvar > D),F2:((proces634752977rocess @ A) > D),F3:(A > (((proces554692349s_term @ A) @ Pvar) > (D > D))),F4:(((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > (D > (D > D)))),X31:A,X32:((proces554692349s_term @ A) @ Pvar)]: ((((((((((proces2117273769s_term @ Pvar) @ D) @ A) @ F1) @ F2) @ F3) @ F4) @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ X31) @ X32)) = (((F3 @ X31) @ X32) @ ((((((((proces2117273769s_term @ Pvar) @ D) @ A) @ F1) @ F2) @ F3) @ F4) @ X32)))))).
% 3.45/1.76 thf(fact_32_process__term_Osimps_I21_J, axiom, (! [A:$tType,D:$tType,Pvar:$tType,F1:(Pvar > D),F2:((proces634752977rocess @ A) > D),F3:(A > (((proces554692349s_term @ A) @ Pvar) > (D > D))),F4:(((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > (D > (D > D)))),X1:Pvar]: ((((((((((proces2117273769s_term @ Pvar) @ D) @ A) @ F1) @ F2) @ F3) @ F4) @ (((proces1627516585ss_VAR @ Pvar) @ A) @ X1)) = (F1 @ X1))))).
% 3.45/1.76 thf(fact_33_process__term_Osimps_I20_J, axiom, (! [B:$tType,Pvar:$tType,A:$tType,F1:(Pvar > B),F2:((proces634752977rocess @ A) > B),F3:(A > (((proces554692349s_term @ A) @ Pvar) > B)),F4:(((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > B)),X41:((proces554692349s_term @ A) @ Pvar),X42:((proces554692349s_term @ A) @ Pvar)]: ((((((((((proces460752237s_term @ Pvar) @ B) @ A) @ F1) @ F2) @ F3) @ F4) @ ((((proces89589571ess_CH @ A) @ Pvar) @ X41) @ X42)) = ((F4 @ X41) @ X42))))).
% 3.45/1.76 thf(fact_34_process__term_Osimps_I19_J, axiom, (! [B:$tType,Pvar:$tType,A:$tType,F1:(Pvar > B),F2:((proces634752977rocess @ A) > B),F3:(A > (((proces554692349s_term @ A) @ Pvar) > B)),F4:(((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > B)),X31:A,X32:((proces554692349s_term @ A) @ Pvar)]: ((((((((((proces460752237s_term @ Pvar) @ B) @ A) @ F1) @ F2) @ F3) @ F4) @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ X31) @ X32)) = ((F3 @ X31) @ X32))))).
% 3.45/1.76 thf(fact_35_process__term_Osimps_I17_J, axiom, (! [A:$tType,B:$tType,Pvar:$tType,F1:(Pvar > B),F2:((proces634752977rocess @ A) > B),F3:(A > (((proces554692349s_term @ A) @ Pvar) > B)),F4:(((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > B)),X1:Pvar]: ((((((((((proces460752237s_term @ Pvar) @ B) @ A) @ F1) @ F2) @ F3) @ F4) @ (((proces1627516585ss_VAR @ Pvar) @ A) @ X1)) = (F1 @ X1))))).
% 3.45/1.76 thf(fact_36_process__term_Odistinct_I11_J, axiom, (! [Pvar:$tType,A:$tType,X31:A,X32:((proces554692349s_term @ A) @ Pvar),X41:((proces554692349s_term @ A) @ Pvar),X42:((proces554692349s_term @ A) @ Pvar)]: ((((((proces1454156180ss_ACT @ A) @ Pvar) @ X31) @ X32) != ((((proces89589571ess_CH @ A) @ Pvar) @ X41) @ X42))))).
% 3.45/1.76 thf(fact_37_process__term_Odistinct_I5_J, axiom, (! [Pvar:$tType,A:$tType,X1:Pvar,X41:((proces554692349s_term @ A) @ Pvar),X42:((proces554692349s_term @ A) @ Pvar)]: (((((proces1627516585ss_VAR @ Pvar) @ A) @ X1) != ((((proces89589571ess_CH @ A) @ Pvar) @ X41) @ X42))))).
% 3.45/1.76 thf(fact_38_process__term_Odistinct_I3_J, axiom, (! [Pvar:$tType,A:$tType,X1:Pvar,X31:A,X32:((proces554692349s_term @ A) @ Pvar)]: (((((proces1627516585ss_VAR @ Pvar) @ A) @ X1) != ((((proces1454156180ss_ACT @ A) @ Pvar) @ X31) @ X32))))).
% 3.45/1.76 thf(fact_39_isACT__VAR, axiom, (! [C:$tType,B:$tType,A:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),X3:A]: ((((((proces1121166967uarded @ A) @ B) @ A) @ Sys) => (((((((proces687458811_isACT @ A) @ B) @ A) @ C) @ Sys) @ (((proces1627516585ss_VAR @ A) @ C) @ X3)) = ((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ (Sys @ X3))))))).
% 3.45/1.76 thf(fact_40_CH2_Oinduct, axiom, (! [A:$tType,B:$tType,P3:((A > ((proces554692349s_term @ B) @ A)) > (((proces554692349s_term @ B) @ A) > $o)),A0:(A > ((proces554692349s_term @ B) @ A)),A1:((proces554692349s_term @ B) @ A)]: (((! [Sys2:(A > ((proces554692349s_term @ B) @ A)),X4:A]: (((P3 @ Sys2) @ (((proces1627516585ss_VAR @ A) @ B) @ X4)))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ A)),P4:(proces634752977rocess @ B)]: (((P3 @ Sys2) @ (((proces1062592052s_PROC @ B) @ A) @ P4)))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ A)),T12:((proces554692349s_term @ B) @ A),T23:((proces554692349s_term @ B) @ A)]: (((P3 @ Sys2) @ ((((proces89589571ess_CH @ B) @ A) @ T12) @ T23)))) => ((! [A3:(A > ((proces554692349s_term @ B) @ A)),V:B,Va:((proces554692349s_term @ B) @ A)]: (((P3 @ A3) @ ((((proces1454156180ss_ACT @ B) @ A) @ V) @ Va)))) => ((P3 @ A0) @ A1)))))))).
% 3.45/1.76 thf(fact_41_CONT_Oinduct, axiom, (! [A:$tType,B:$tType,P3:((A > ((proces554692349s_term @ B) @ A)) > (((proces554692349s_term @ B) @ A) > $o)),A0:(A > ((proces554692349s_term @ B) @ A)),A1:((proces554692349s_term @ B) @ A)]: (((! [Sys2:(A > ((proces554692349s_term @ B) @ A)),X4:A]: (((P3 @ Sys2) @ (((proces1627516585ss_VAR @ A) @ B) @ X4)))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ A)),P4:(proces634752977rocess @ B)]: (((P3 @ Sys2) @ (((proces1062592052s_PROC @ B) @ A) @ P4)))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ A)),A3:B,T3:((proces554692349s_term @ B) @ A)]: (((P3 @ Sys2) @ ((((proces1454156180ss_ACT @ B) @ A) @ A3) @ T3)))) => ((! [A3:(A > ((proces554692349s_term @ B) @ A)),V:((proces554692349s_term @ B) @ A),Va:((proces554692349s_term @ B) @ A)]: (((P3 @ A3) @ ((((proces89589571ess_CH @ B) @ A) @ V) @ Va)))) => ((P3 @ A0) @ A1)))))))).
% 3.45/1.76 thf(fact_42_PREF_Oinduct, axiom, (! [C:$tType,A:$tType,B:$tType,P3:((A > ((proces554692349s_term @ B) @ C)) > (((proces554692349s_term @ B) @ A) > $o)),A0:(A > ((proces554692349s_term @ B) @ C)),A1:((proces554692349s_term @ B) @ A)]: (((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),X4:A]: (((P3 @ Sys2) @ (((proces1627516585ss_VAR @ A) @ B) @ X4)))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),P4:(proces634752977rocess @ B)]: (((P3 @ Sys2) @ (((proces1062592052s_PROC @ B) @ A) @ P4)))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),A3:B,T3:((proces554692349s_term @ B) @ A)]: (((P3 @ Sys2) @ ((((proces1454156180ss_ACT @ B) @ A) @ A3) @ T3)))) => ((! [A3:(A > ((proces554692349s_term @ B) @ C)),V:((proces554692349s_term @ B) @ A),Va:((proces554692349s_term @ B) @ A)]: (((P3 @ A3) @ ((((proces89589571ess_CH @ B) @ A) @ V) @ Va)))) => ((P3 @ A0) @ A1)))))))).
% 3.45/1.76 thf(fact_43_guarded__def, axiom, (! [C:$tType,B:$tType,A:$tType]: (((((proces1121166967uarded @ A) @ B) @ C) = (^ [Sys3:(A > ((proces554692349s_term @ B) @ C))]: ((! [X5:A,Y:C]: (((Sys3 @ X5) != (((proces1627516585ss_VAR @ C) @ B) @ Y)))))))))).
% 3.45/1.76 thf(fact_44_isACT_Oinduct, axiom, (! [B:$tType,C:$tType,A:$tType,D:$tType,P3:((A > ((proces554692349s_term @ B) @ C)) > (((proces554692349s_term @ D) @ A) > $o)),A0:(A > ((proces554692349s_term @ B) @ C)),A1:((proces554692349s_term @ D) @ A)]: (((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),X4:A]: (((P3 @ Sys2) @ (((proces1627516585ss_VAR @ A) @ D) @ X4)))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),P4:(proces634752977rocess @ D)]: (((P3 @ Sys2) @ (((proces1062592052s_PROC @ D) @ A) @ P4)))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),A3:D,T3:((proces554692349s_term @ D) @ A)]: (((P3 @ Sys2) @ ((((proces1454156180ss_ACT @ D) @ A) @ A3) @ T3)))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),T12:((proces554692349s_term @ D) @ A),T23:((proces554692349s_term @ D) @ A)]: (((P3 @ Sys2) @ ((((proces89589571ess_CH @ D) @ A) @ T12) @ T23)))) => ((P3 @ A0) @ A1)))))))).
% 3.45/1.76 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P3:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P3)) = (P3 @ A2))))).
% 3.45/1.76 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A4:(set @ A)]: ((((collect @ A) @ (^ [X:A]: ((((member @ A) @ X) @ A4)))) = A4)))).
% 3.45/1.76 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P3:(A > $o),Q:(A > $o)]: (((! [X6:A]: (((P3 @ X6) = (Q @ X6)))) => (((collect @ A) @ P3) = ((collect @ A) @ Q)))))).
% 3.45/1.76 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X6:A]: (((F @ X6) = (G @ X6)))) => (F = G))))).
% 3.45/1.76 thf(fact_49_process__term_Oinduct, axiom, (! [Pvar:$tType,A:$tType,P3:(((proces554692349s_term @ A) @ Pvar) > $o),Process_term:((proces554692349s_term @ A) @ Pvar)]: (((! [X6:Pvar]: ((P3 @ (((proces1627516585ss_VAR @ Pvar) @ A) @ X6)))) => ((! [X6:(proces634752977rocess @ A)]: ((P3 @ (((proces1062592052s_PROC @ A) @ Pvar) @ X6)))) => ((! [X1a:A,X2a:((proces554692349s_term @ A) @ Pvar)]: (((P3 @ X2a) => (P3 @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ X1a) @ X2a))))) => ((! [X1a:((proces554692349s_term @ A) @ Pvar),X2a:((proces554692349s_term @ A) @ Pvar)]: (((P3 @ X1a) => ((P3 @ X2a) => (P3 @ ((((proces89589571ess_CH @ A) @ Pvar) @ X1a) @ X2a)))))) => (P3 @ Process_term)))))))).
% 3.45/1.76 thf(fact_50_process__term_Oexhaust, axiom, (! [Pvar:$tType,A:$tType,Y3:((proces554692349s_term @ A) @ Pvar)]: (((! [X13:Pvar]: ((Y3 != (((proces1627516585ss_VAR @ Pvar) @ A) @ X13)))) => ((! [X23:(proces634752977rocess @ A)]: ((Y3 != (((proces1062592052s_PROC @ A) @ Pvar) @ X23)))) => ((! [X312:A,X322:((proces554692349s_term @ A) @ Pvar)]: ((Y3 != ((((proces1454156180ss_ACT @ A) @ Pvar) @ X312) @ X322)))) => (~ ((! [X412:((proces554692349s_term @ A) @ Pvar),X422:((proces554692349s_term @ A) @ Pvar)]: ((Y3 != ((((proces89589571ess_CH @ A) @ Pvar) @ X412) @ X422)))))))))))).
% 3.45/1.76 thf(fact_51_solution_Osimps_I3_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T2:((proces554692349s_term @ B) @ A)]: ((((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ T2) => (((proces745025900prefOf @ B) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ T2)) = (((((proces1708129104e_PREF @ A) @ B) @ A) @ Sys) @ T2)))))).
% 3.45/1.76 thf(fact_52_process__term_Opred__True, axiom, (! [B:$tType,A:$tType]: ((((((proces2118920028s_term @ A) @ B) @ (^ [Uu:A]: ($true))) @ (^ [Uu:B]: ($true))) = (^ [Uu:((proces554692349s_term @ A) @ B)]: ($true)))))).
% 3.45/1.76 thf(fact_53_process_Opred__True, axiom, (! [A:$tType]: ((((proces1205983068rocess @ A) @ (^ [Uu:A]: ($true))) = (^ [Uu:(proces634752977rocess @ A)]: ($true)))))).
% 3.45/1.76 thf(fact_54_PREF_Oelims, axiom, (! [A:$tType,C:$tType,B:$tType,X7:(A > ((proces554692349s_term @ B) @ C)),Xa:((proces554692349s_term @ B) @ A),Y3:B]: ((((((((proces1708129104e_PREF @ A) @ B) @ C) @ X7) @ Xa) = Y3) => ((! [X4:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ B) @ X4)) => (Y3 != ((((((((proces460752237s_term @ C) @ B) @ B) @ (^ [Aa3:C]: ((undefined @ B)))) @ (proces745025900prefOf @ B)) @ (^ [A5:B,T4:((proces554692349s_term @ B) @ C)]: (A5))) @ (^ [Aa3:((proces554692349s_term @ B) @ C),Ab:((proces554692349s_term @ B) @ C)]: ((undefined @ B)))) @ (X7 @ X4)))))) => ((! [P4:(proces634752977rocess @ B)]: (((Xa = (((proces1062592052s_PROC @ B) @ A) @ P4)) => (Y3 != ((proces745025900prefOf @ B) @ P4))))) => ((! [A3:B]: (((? [T3:((proces554692349s_term @ B) @ A)]: ((Xa = ((((proces1454156180ss_ACT @ B) @ A) @ A3) @ T3)))) => (Y3 != A3)))) => (~ (((? [V:((proces554692349s_term @ B) @ A),Va:((proces554692349s_term @ B) @ A)]: ((Xa = ((((proces89589571ess_CH @ B) @ A) @ V) @ Va)))) => (Y3 != (undefined @ B)))))))))))).
% 3.45/1.76 thf(fact_55_isACT_Oelims_I1_J, axiom, (! [D:$tType,A:$tType,B:$tType,C:$tType,X7:(A > ((proces554692349s_term @ B) @ C)),Xa:((proces554692349s_term @ D) @ A),Y3:$o]: (((((((((proces687458811_isACT @ A) @ B) @ C) @ D) @ X7) @ Xa) = Y3) => ((! [X4:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ D) @ X4)) => (Y3 = (~ (((((((((proces460752237s_term @ C) @ $o) @ B) @ (^ [Pvar2:C]: ($false))) @ (proces10484146Action @ B)) @ (^ [A5:B,T4:((proces554692349s_term @ B) @ C)]: ($true))) @ (^ [Process_term1:((proces554692349s_term @ B) @ C),Process_term2:((proces554692349s_term @ B) @ C)]: ($false))) @ (X7 @ X4)))))))) => ((! [P4:(proces634752977rocess @ D)]: (((Xa = (((proces1062592052s_PROC @ D) @ A) @ P4)) => (Y3 = (~ (((proces10484146Action @ D) @ P4))))))) => (((? [A3:D,T3:((proces554692349s_term @ D) @ A)]: ((Xa = ((((proces1454156180ss_ACT @ D) @ A) @ A3) @ T3)))) => (~ (Y3))) => (~ (((? [T12:((proces554692349s_term @ D) @ A),T23:((proces554692349s_term @ D) @ A)]: ((Xa = ((((proces89589571ess_CH @ D) @ A) @ T12) @ T23)))) => Y3)))))))))).
% 3.45/1.76 thf(fact_56_PREF_Osimps_I1_J, axiom, (! [B:$tType,C:$tType,A:$tType,Sys:(A > ((proces554692349s_term @ B) @ C)),X3:A]: (((((((proces1708129104e_PREF @ A) @ B) @ C) @ Sys) @ (((proces1627516585ss_VAR @ A) @ B) @ X3)) = ((((((((proces460752237s_term @ C) @ B) @ B) @ (^ [Aa3:C]: ((undefined @ B)))) @ (proces745025900prefOf @ B)) @ (^ [A5:B,T4:((proces554692349s_term @ B) @ C)]: (A5))) @ (^ [Aa3:((proces554692349s_term @ B) @ C),Ab:((proces554692349s_term @ B) @ C)]: ((undefined @ B)))) @ (Sys @ X3)))))).
% 3.45/1.76 thf(fact_57_isACT_Oelims_I2_J, axiom, (! [C:$tType,B:$tType,A:$tType,D:$tType,X7:(A > ((proces554692349s_term @ B) @ C)),Xa:((proces554692349s_term @ D) @ A)]: ((((((((proces687458811_isACT @ A) @ B) @ C) @ D) @ X7) @ Xa) => ((! [X4:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ D) @ X4)) => (~ (((((((((proces460752237s_term @ C) @ $o) @ B) @ (^ [Pvar2:C]: ($false))) @ (proces10484146Action @ B)) @ (^ [A5:B,T4:((proces554692349s_term @ B) @ C)]: ($true))) @ (^ [Process_term1:((proces554692349s_term @ B) @ C),Process_term2:((proces554692349s_term @ B) @ C)]: ($false))) @ (X7 @ X4))))))) => ((! [P4:(proces634752977rocess @ D)]: (((Xa = (((proces1062592052s_PROC @ D) @ A) @ P4)) => (~ (((proces10484146Action @ D) @ P4)))))) => (~ ((! [A3:D,T3:((proces554692349s_term @ D) @ A)]: ((Xa != ((((proces1454156180ss_ACT @ D) @ A) @ A3) @ T3)))))))))))).
% 3.45/1.76 thf(fact_58_isACT_Oelims_I3_J, axiom, (! [C:$tType,B:$tType,A:$tType,D:$tType,X7:(A > ((proces554692349s_term @ B) @ C)),Xa:((proces554692349s_term @ D) @ A)]: (((~ (((((((proces687458811_isACT @ A) @ B) @ C) @ D) @ X7) @ Xa))) => ((! [X4:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ D) @ X4)) => ((((((((proces460752237s_term @ C) @ $o) @ B) @ (^ [Pvar2:C]: ($false))) @ (proces10484146Action @ B)) @ (^ [A5:B,T4:((proces554692349s_term @ B) @ C)]: ($true))) @ (^ [Process_term1:((proces554692349s_term @ B) @ C),Process_term2:((proces554692349s_term @ B) @ C)]: ($false))) @ (X7 @ X4))))) => ((! [P4:(proces634752977rocess @ D)]: (((Xa = (((proces1062592052s_PROC @ D) @ A) @ P4)) => ((proces10484146Action @ D) @ P4)))) => (~ ((! [T12:((proces554692349s_term @ D) @ A),T23:((proces554692349s_term @ D) @ A)]: ((Xa != ((((proces89589571ess_CH @ D) @ A) @ T12) @ T23)))))))))))).
% 3.45/1.76 thf(fact_59_solution_Osimps_I4_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T2:((proces554692349s_term @ B) @ A)]: ((((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ T2) => (((proces1778668539contOf @ B) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ T2)) = ((((proces1652378886lution @ A) @ B) @ Sys) @ ((((proces126235999e_CONT @ A) @ B) @ Sys) @ T2))))))).
% 3.45/1.76 thf(fact_60_CH2_Ocases, axiom, (! [A:$tType,B:$tType,X7:((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))]: (((! [Sys2:(A > ((proces554692349s_term @ B) @ A)),X4:A]: ((X7 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ Sys2) @ (((proces1627516585ss_VAR @ A) @ B) @ X4))))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ A)),P4:(proces634752977rocess @ B)]: ((X7 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ Sys2) @ (((proces1062592052s_PROC @ B) @ A) @ P4))))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ A)),T12:((proces554692349s_term @ B) @ A),T23:((proces554692349s_term @ B) @ A)]: ((X7 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ Sys2) @ ((((proces89589571ess_CH @ B) @ A) @ T12) @ T23))))) => (~ ((! [A3:(A > ((proces554692349s_term @ B) @ A)),V:B,Va:((proces554692349s_term @ B) @ A)]: ((X7 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ A3) @ ((((proces1454156180ss_ACT @ B) @ A) @ V) @ Va))))))))))))).
% 3.45/1.76 thf(fact_61_CONT_Ocases, axiom, (! [A:$tType,B:$tType,X7:((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))]: (((! [Sys2:(A > ((proces554692349s_term @ B) @ A)),X4:A]: ((X7 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ Sys2) @ (((proces1627516585ss_VAR @ A) @ B) @ X4))))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ A)),P4:(proces634752977rocess @ B)]: ((X7 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ Sys2) @ (((proces1062592052s_PROC @ B) @ A) @ P4))))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ A)),A3:B,T3:((proces554692349s_term @ B) @ A)]: ((X7 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ Sys2) @ ((((proces1454156180ss_ACT @ B) @ A) @ A3) @ T3))))) => (~ ((! [A3:(A > ((proces554692349s_term @ B) @ A)),V:((proces554692349s_term @ B) @ A),Va:((proces554692349s_term @ B) @ A)]: ((X7 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ A3) @ ((((proces89589571ess_CH @ B) @ A) @ V) @ Va))))))))))))).
% 3.45/1.76 thf(fact_62_PREF_Ocases, axiom, (! [C:$tType,A:$tType,B:$tType,X7:((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A))]: (((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),X4:A]: ((X7 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A)) @ Sys2) @ (((proces1627516585ss_VAR @ A) @ B) @ X4))))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),P4:(proces634752977rocess @ B)]: ((X7 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A)) @ Sys2) @ (((proces1062592052s_PROC @ B) @ A) @ P4))))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),A3:B,T3:((proces554692349s_term @ B) @ A)]: ((X7 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A)) @ Sys2) @ ((((proces1454156180ss_ACT @ B) @ A) @ A3) @ T3))))) => (~ ((! [A3:(A > ((proces554692349s_term @ B) @ C)),V:((proces554692349s_term @ B) @ A),Va:((proces554692349s_term @ B) @ A)]: ((X7 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A)) @ A3) @ ((((proces89589571ess_CH @ B) @ A) @ V) @ Va))))))))))))).
% 3.45/1.76 thf(fact_63_isACT_Ocases, axiom, (! [B:$tType,C:$tType,A:$tType,D:$tType,X7:((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))]: (((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),X4:A]: ((X7 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ Sys2) @ (((proces1627516585ss_VAR @ A) @ D) @ X4))))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),P4:(proces634752977rocess @ D)]: ((X7 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ Sys2) @ (((proces1062592052s_PROC @ D) @ A) @ P4))))) => ((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),A3:D,T3:((proces554692349s_term @ D) @ A)]: ((X7 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ Sys2) @ ((((proces1454156180ss_ACT @ D) @ A) @ A3) @ T3))))) => (~ ((! [Sys2:(A > ((proces554692349s_term @ B) @ C)),T12:((proces554692349s_term @ D) @ A),T23:((proces554692349s_term @ D) @ A)]: ((X7 != ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ Sys2) @ ((((proces89589571ess_CH @ D) @ A) @ T12) @ T23))))))))))))).
% 3.45/1.76 thf(fact_64_solution_Odisc__iff_I1_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T2:((proces554692349s_term @ B) @ A)]: ((((proces10484146Action @ B) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ T2)) = ((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ T2))))).
% 3.45/1.76 thf(fact_65_process_Ocollapse_I1_J, axiom, (! [A:$tType,Process:(proces634752977rocess @ A)]: ((((proces10484146Action @ A) @ Process) => ((((proces1525233512Action @ A) @ ((proces745025900prefOf @ A) @ Process)) @ ((proces1778668539contOf @ A) @ Process)) = Process))))).
% 3.45/1.76 thf(fact_66_contOf__def, axiom, (! [A:$tType]: (((proces1778668539contOf @ A) = ((((proces1406508781rocess @ A) @ (proces634752977rocess @ A)) @ (^ [X112:A,X123:(proces634752977rocess @ A)]: (X123))) @ (^ [Uu2:(proces634752977rocess @ A),Uv:(proces634752977rocess @ A)]: ((undefined @ (proces634752977rocess @ A))))))))).
% 3.45/1.76 thf(fact_67_process_Odisc__eq__case_I1_J, axiom, (! [A:$tType]: (((proces10484146Action @ A) = ((((proces1406508781rocess @ A) @ $o) @ (^ [Uu:A,Uv2:(proces634752977rocess @ A)]: ($true))) @ (^ [Uu:(proces634752977rocess @ A),Uv2:(proces634752977rocess @ A)]: ($false))))))).
% 3.45/1.76 thf(fact_68_isAction__def, axiom, (! [A:$tType]: (((proces10484146Action @ A) = (^ [Process2:(proces634752977rocess @ A)]: ((? [X112:A,X123:(proces634752977rocess @ A)]: ((Process2 = (((proces1525233512Action @ A) @ X112) @ X123)))))))))).
% 3.45/1.76 thf(fact_69_process_OdiscI_I1_J, axiom, (! [A:$tType,Process:(proces634752977rocess @ A),X11:A,X122:(proces634752977rocess @ A)]: (((Process = (((proces1525233512Action @ A) @ X11) @ X122)) => ((proces10484146Action @ A) @ Process))))).
% 3.45/1.76 thf(fact_70_process_Odisc_I1_J, axiom, (! [A:$tType,X11:A,X122:(proces634752977rocess @ A)]: (((proces10484146Action @ A) @ (((proces1525233512Action @ A) @ X11) @ X122))))).
% 3.45/1.76 thf(fact_71_process_Osel_I2_J, axiom, (! [A:$tType,X11:A,X122:(proces634752977rocess @ A)]: ((((proces1778668539contOf @ A) @ (((proces1525233512Action @ A) @ X11) @ X122)) = X122)))).
% 3.45/1.76 thf(fact_72_CONT_Osimps_I1_J, axiom, (! [B:$tType,A:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),X3:A]: ((((((proces126235999e_CONT @ A) @ B) @ Sys) @ (((proces1627516585ss_VAR @ A) @ B) @ X3)) = ((((((((proces460752237s_term @ A) @ ((proces554692349s_term @ B) @ A)) @ B) @ (^ [Aa3:A]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [P5:(proces634752977rocess @ B)]: ((((proces1062592052s_PROC @ B) @ A) @ ((proces1778668539contOf @ B) @ P5))))) @ (^ [A5:B,T4:((proces554692349s_term @ B) @ A)]: (T4))) @ (^ [Aa3:((proces554692349s_term @ B) @ A),Ab:((proces554692349s_term @ B) @ A)]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (Sys @ X3)))))).
% 3.45/1.76 thf(fact_73_isACT_Osimps_I2_J, axiom, (! [A:$tType,C:$tType,B:$tType,D:$tType,Sys:(A > ((proces554692349s_term @ B) @ C)),P:(proces634752977rocess @ D)]: ((((((((proces687458811_isACT @ A) @ B) @ C) @ D) @ Sys) @ (((proces1062592052s_PROC @ D) @ A) @ P)) = ((proces10484146Action @ D) @ P))))).
% 3.45/1.76 thf(fact_74_solution_Odisc_I1_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T2:((proces554692349s_term @ B) @ A)]: ((((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ T2) => ((proces10484146Action @ B) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ T2)))))).
% 3.45/1.76 thf(fact_75_isACT_Osimps_I1_J, axiom, (! [D:$tType,B:$tType,C:$tType,A:$tType,Sys:(A > ((proces554692349s_term @ B) @ C)),X3:A]: ((((((((proces687458811_isACT @ A) @ B) @ C) @ D) @ Sys) @ (((proces1627516585ss_VAR @ A) @ D) @ X3)) = ((((((((proces460752237s_term @ C) @ $o) @ B) @ (^ [Pvar2:C]: ($false))) @ (proces10484146Action @ B)) @ (^ [A5:B,T4:((proces554692349s_term @ B) @ C)]: ($true))) @ (^ [Process_term1:((proces554692349s_term @ B) @ C),Process_term2:((proces554692349s_term @ B) @ C)]: ($false))) @ (Sys @ X3)))))).
% 3.45/1.76 thf(fact_76_CONT_Osimps_I2_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),P:(proces634752977rocess @ B)]: ((((((proces126235999e_CONT @ A) @ B) @ Sys) @ (((proces1062592052s_PROC @ B) @ A) @ P)) = (((proces1062592052s_PROC @ B) @ A) @ ((proces1778668539contOf @ B) @ P)))))).
% 3.45/1.76 thf(fact_77_prefOf__def, axiom, (! [A:$tType]: (((proces745025900prefOf @ A) = ((((proces1406508781rocess @ A) @ A) @ (^ [X112:A,X123:(proces634752977rocess @ A)]: (X112))) @ (^ [Uu2:(proces634752977rocess @ A),Uv:(proces634752977rocess @ A)]: ((undefined @ A)))))))).
% 3.45/1.76 thf(fact_78_CONT_Oelims, axiom, (! [A:$tType,B:$tType,X7:(A > ((proces554692349s_term @ B) @ A)),Xa:((proces554692349s_term @ B) @ A),Y3:((proces554692349s_term @ B) @ A)]: (((((((proces126235999e_CONT @ A) @ B) @ X7) @ Xa) = Y3) => ((! [X4:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ B) @ X4)) => (Y3 != ((((((((proces460752237s_term @ A) @ ((proces554692349s_term @ B) @ A)) @ B) @ (^ [Aa3:A]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [P5:(proces634752977rocess @ B)]: ((((proces1062592052s_PROC @ B) @ A) @ ((proces1778668539contOf @ B) @ P5))))) @ (^ [A5:B,T4:((proces554692349s_term @ B) @ A)]: (T4))) @ (^ [Aa3:((proces554692349s_term @ B) @ A),Ab:((proces554692349s_term @ B) @ A)]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (X7 @ X4)))))) => ((! [P4:(proces634752977rocess @ B)]: (((Xa = (((proces1062592052s_PROC @ B) @ A) @ P4)) => (Y3 != (((proces1062592052s_PROC @ B) @ A) @ ((proces1778668539contOf @ B) @ P4)))))) => ((! [A3:B,T3:((proces554692349s_term @ B) @ A)]: (((Xa = ((((proces1454156180ss_ACT @ B) @ A) @ A3) @ T3)) => (Y3 != T3)))) => (~ (((? [V:((proces554692349s_term @ B) @ A),Va:((proces554692349s_term @ B) @ A)]: ((Xa = ((((proces89589571ess_CH @ B) @ A) @ V) @ Va)))) => (Y3 != (undefined @ ((proces554692349s_term @ B) @ A))))))))))))).
% 3.45/1.76 thf(fact_79_old_Oprod_Oinject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A6:A,B3:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A6) @ B3)) = ((A2 = A6) & (B2 = B3)))))).
% 3.45/1.76 thf(fact_80_prod_Oinject, axiom, (! [A:$tType,B:$tType,X1:A,X2:B,Y1:A,Y2:B]: (((((((product_Pair @ A) @ B) @ X1) @ X2) = ((((product_Pair @ A) @ B) @ Y1) @ Y2)) = ((X1 = Y1) & (X2 = Y2)))))).
% 3.45/1.76 thf(fact_81_PREF_Opelims, axiom, (! [C:$tType,A:$tType,B:$tType,X7:(A > ((proces554692349s_term @ B) @ C)),Xa:((proces554692349s_term @ B) @ A),Y3:B]: ((((((((proces1708129104e_PREF @ A) @ B) @ C) @ X7) @ Xa) = Y3) => ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A))) @ (((proces527360425EF_rel @ A) @ B) @ C)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A)) @ X7) @ Xa)) => ((! [X4:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ B) @ X4)) => ((Y3 = ((((((((proces460752237s_term @ C) @ B) @ B) @ (^ [Aa3:C]: ((undefined @ B)))) @ (proces745025900prefOf @ B)) @ (^ [A5:B,T4:((proces554692349s_term @ B) @ C)]: (A5))) @ (^ [Aa3:((proces554692349s_term @ B) @ C),Ab:((proces554692349s_term @ B) @ C)]: ((undefined @ B)))) @ (X7 @ X4))) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A))) @ (((proces527360425EF_rel @ A) @ B) @ C)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A)) @ X7) @ (((proces1627516585ss_VAR @ A) @ B) @ X4))))))))) => ((! [P4:(proces634752977rocess @ B)]: (((Xa = (((proces1062592052s_PROC @ B) @ A) @ P4)) => ((Y3 = ((proces745025900prefOf @ B) @ P4)) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A))) @ (((proces527360425EF_rel @ A) @ B) @ C)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A)) @ X7) @ (((proces1062592052s_PROC @ B) @ A) @ P4))))))))) => ((! [A3:B,T3:((proces554692349s_term @ B) @ A)]: (((Xa = ((((proces1454156180ss_ACT @ B) @ A) @ A3) @ T3)) => ((Y3 = A3) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A))) @ (((proces527360425EF_rel @ A) @ B) @ C)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A)) @ X7) @ ((((proces1454156180ss_ACT @ B) @ A) @ A3) @ T3))))))))) => (~ ((! [V:((proces554692349s_term @ B) @ A),Va:((proces554692349s_term @ B) @ A)]: (((Xa = ((((proces89589571ess_CH @ B) @ A) @ V) @ Va)) => ((Y3 = (undefined @ B)) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A))) @ (((proces527360425EF_rel @ A) @ B) @ C)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ B) @ A)) @ X7) @ ((((proces89589571ess_CH @ B) @ A) @ V) @ Va))))))))))))))))))).
% 3.45/1.76 thf(fact_82_CONT_Opelims, axiom, (! [A:$tType,B:$tType,X7:(A > ((proces554692349s_term @ B) @ A)),Xa:((proces554692349s_term @ B) @ A),Y3:((proces554692349s_term @ B) @ A)]: (((((((proces126235999e_CONT @ A) @ B) @ X7) @ Xa) = Y3) => ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces1004198490NT_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X7) @ Xa)) => ((! [X4:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ B) @ X4)) => ((Y3 = ((((((((proces460752237s_term @ A) @ ((proces554692349s_term @ B) @ A)) @ B) @ (^ [Aa3:A]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [P5:(proces634752977rocess @ B)]: ((((proces1062592052s_PROC @ B) @ A) @ ((proces1778668539contOf @ B) @ P5))))) @ (^ [A5:B,T4:((proces554692349s_term @ B) @ A)]: (T4))) @ (^ [Aa3:((proces554692349s_term @ B) @ A),Ab:((proces554692349s_term @ B) @ A)]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (X7 @ X4))) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces1004198490NT_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X7) @ (((proces1627516585ss_VAR @ A) @ B) @ X4))))))))) => ((! [P4:(proces634752977rocess @ B)]: (((Xa = (((proces1062592052s_PROC @ B) @ A) @ P4)) => ((Y3 = (((proces1062592052s_PROC @ B) @ A) @ ((proces1778668539contOf @ B) @ P4))) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces1004198490NT_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X7) @ (((proces1062592052s_PROC @ B) @ A) @ P4))))))))) => ((! [A3:B,T3:((proces554692349s_term @ B) @ A)]: (((Xa = ((((proces1454156180ss_ACT @ B) @ A) @ A3) @ T3)) => ((Y3 = T3) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces1004198490NT_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X7) @ ((((proces1454156180ss_ACT @ B) @ A) @ A3) @ T3))))))))) => (~ ((! [V:((proces554692349s_term @ B) @ A),Va:((proces554692349s_term @ B) @ A)]: (((Xa = ((((proces89589571ess_CH @ B) @ A) @ V) @ Va)) => ((Y3 = (undefined @ ((proces554692349s_term @ B) @ A))) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces1004198490NT_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X7) @ ((((proces89589571ess_CH @ B) @ A) @ V) @ Va))))))))))))))))))).
% 3.45/1.76 thf(fact_83_isACT_Opelims_I1_J, axiom, (! [B:$tType,C:$tType,A:$tType,D:$tType,X7:(A > ((proces554692349s_term @ B) @ C)),Xa:((proces554692349s_term @ D) @ A),Y3:$o]: (((((((((proces687458811_isACT @ A) @ B) @ C) @ D) @ X7) @ Xa) = Y3) => ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))) @ ((((proces896239806CT_rel @ A) @ B) @ C) @ D)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ X7) @ Xa)) => ((! [X4:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ D) @ X4)) => ((Y3 = ((((((((proces460752237s_term @ C) @ $o) @ B) @ (^ [Pvar2:C]: ($false))) @ (proces10484146Action @ B)) @ (^ [A5:B,T4:((proces554692349s_term @ B) @ C)]: ($true))) @ (^ [Process_term1:((proces554692349s_term @ B) @ C),Process_term2:((proces554692349s_term @ B) @ C)]: ($false))) @ (X7 @ X4))) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))) @ ((((proces896239806CT_rel @ A) @ B) @ C) @ D)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ X7) @ (((proces1627516585ss_VAR @ A) @ D) @ X4))))))))) => ((! [P4:(proces634752977rocess @ D)]: (((Xa = (((proces1062592052s_PROC @ D) @ A) @ P4)) => ((Y3 = ((proces10484146Action @ D) @ P4)) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))) @ ((((proces896239806CT_rel @ A) @ B) @ C) @ D)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ X7) @ (((proces1062592052s_PROC @ D) @ A) @ P4))))))))) => ((! [A3:D,T3:((proces554692349s_term @ D) @ A)]: (((Xa = ((((proces1454156180ss_ACT @ D) @ A) @ A3) @ T3)) => (Y3 => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))) @ ((((proces896239806CT_rel @ A) @ B) @ C) @ D)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ X7) @ ((((proces1454156180ss_ACT @ D) @ A) @ A3) @ T3))))))))) => (~ ((! [T12:((proces554692349s_term @ D) @ A),T23:((proces554692349s_term @ D) @ A)]: (((Xa = ((((proces89589571ess_CH @ D) @ A) @ T12) @ T23)) => ((~ (Y3)) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))) @ ((((proces896239806CT_rel @ A) @ B) @ C) @ D)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ X7) @ ((((proces89589571ess_CH @ D) @ A) @ T12) @ T23))))))))))))))))))).
% 3.45/1.76 thf(fact_84_isACT_Opelims_I2_J, axiom, (! [B:$tType,C:$tType,A:$tType,D:$tType,X7:(A > ((proces554692349s_term @ B) @ C)),Xa:((proces554692349s_term @ D) @ A)]: ((((((((proces687458811_isACT @ A) @ B) @ C) @ D) @ X7) @ Xa) => ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))) @ ((((proces896239806CT_rel @ A) @ B) @ C) @ D)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ X7) @ Xa)) => ((! [X4:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ D) @ X4)) => ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))) @ ((((proces896239806CT_rel @ A) @ B) @ C) @ D)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ X7) @ (((proces1627516585ss_VAR @ A) @ D) @ X4))) => (~ (((((((((proces460752237s_term @ C) @ $o) @ B) @ (^ [Pvar2:C]: ($false))) @ (proces10484146Action @ B)) @ (^ [A5:B,T4:((proces554692349s_term @ B) @ C)]: ($true))) @ (^ [Process_term1:((proces554692349s_term @ B) @ C),Process_term2:((proces554692349s_term @ B) @ C)]: ($false))) @ (X7 @ X4)))))))) => ((! [P4:(proces634752977rocess @ D)]: (((Xa = (((proces1062592052s_PROC @ D) @ A) @ P4)) => ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))) @ ((((proces896239806CT_rel @ A) @ B) @ C) @ D)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ X7) @ (((proces1062592052s_PROC @ D) @ A) @ P4))) => (~ (((proces10484146Action @ D) @ P4))))))) => (~ ((! [A3:D,T3:((proces554692349s_term @ D) @ A)]: (((Xa = ((((proces1454156180ss_ACT @ D) @ A) @ A3) @ T3)) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))) @ ((((proces896239806CT_rel @ A) @ B) @ C) @ D)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ X7) @ ((((proces1454156180ss_ACT @ D) @ A) @ A3) @ T3))))))))))))))))).
% 3.45/1.76 thf(fact_85_isACT_Opelims_I3_J, axiom, (! [B:$tType,C:$tType,A:$tType,D:$tType,X7:(A > ((proces554692349s_term @ B) @ C)),Xa:((proces554692349s_term @ D) @ A)]: (((~ (((((((proces687458811_isACT @ A) @ B) @ C) @ D) @ X7) @ Xa))) => ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))) @ ((((proces896239806CT_rel @ A) @ B) @ C) @ D)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ X7) @ Xa)) => ((! [X4:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ D) @ X4)) => ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))) @ ((((proces896239806CT_rel @ A) @ B) @ C) @ D)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ X7) @ (((proces1627516585ss_VAR @ A) @ D) @ X4))) => ((((((((proces460752237s_term @ C) @ $o) @ B) @ (^ [Pvar2:C]: ($false))) @ (proces10484146Action @ B)) @ (^ [A5:B,T4:((proces554692349s_term @ B) @ C)]: ($true))) @ (^ [Process_term1:((proces554692349s_term @ B) @ C),Process_term2:((proces554692349s_term @ B) @ C)]: ($false))) @ (X7 @ X4)))))) => ((! [P4:(proces634752977rocess @ D)]: (((Xa = (((proces1062592052s_PROC @ D) @ A) @ P4)) => ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))) @ ((((proces896239806CT_rel @ A) @ B) @ C) @ D)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ X7) @ (((proces1062592052s_PROC @ D) @ A) @ P4))) => ((proces10484146Action @ D) @ P4))))) => (~ ((! [T12:((proces554692349s_term @ D) @ A),T23:((proces554692349s_term @ D) @ A)]: (((Xa = ((((proces89589571ess_CH @ D) @ A) @ T12) @ T23)) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A))) @ ((((proces896239806CT_rel @ A) @ B) @ C) @ D)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ C))) @ ((proces554692349s_term @ D) @ A)) @ X7) @ ((((proces89589571ess_CH @ D) @ A) @ T12) @ T23))))))))))))))))).
% 3.45/1.76 thf(fact_86_surj__pair, axiom, (! [A:$tType,B:$tType,P:((product_prod @ A) @ B)]: ((? [X6:A,Y4:B]: ((P = ((((product_Pair @ A) @ B) @ X6) @ Y4))))))).
% 3.45/1.76 thf(fact_87_prod__cases, axiom, (! [B:$tType,A:$tType,P3:(((product_prod @ A) @ B) > $o),P:((product_prod @ A) @ B)]: (((! [A3:A,B4:B]: ((P3 @ ((((product_Pair @ A) @ B) @ A3) @ B4)))) => (P3 @ P))))).
% 3.45/1.76 thf(fact_88_Pair__inject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A6:A,B3:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A6) @ B3)) => (~ (((A2 = A6) => (B2 != B3)))))))).
% 3.45/1.76 thf(fact_89_prod__cases3, axiom, (! [A:$tType,B:$tType,C:$tType,Y3:((product_prod @ A) @ ((product_prod @ B) @ C))]: ((~ ((! [A3:A,B4:B,C2:C]: ((Y3 != ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A3) @ ((((product_Pair @ B) @ C) @ B4) @ C2)))))))))).
% 3.45/1.76 thf(fact_90_prod__cases4, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,Y3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D)))]: ((~ ((! [A3:A,B4:B,C2:C,D2:D]: ((Y3 != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) @ A3) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D)) @ B4) @ ((((product_Pair @ C) @ D) @ C2) @ D2))))))))))).
% 3.45/1.76 thf(fact_91_prod__cases5, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,Y3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))))]: ((~ ((! [A3:A,B4:B,C2:C,D2:D,E2:E]: ((Y3 != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) @ A3) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ E)) @ C2) @ ((((product_Pair @ D) @ E) @ D2) @ E2)))))))))))).
% 3.45/1.76 thf(fact_92_prod__cases6, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,F5:$tType,Y3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F5)))))]: ((~ ((! [A3:A,B4:B,C2:C,D2:D,E2:E,F6:F5]: ((Y3 != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F5))))) @ A3) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F5)))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F5))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E) @ F5)) @ D2) @ ((((product_Pair @ E) @ F5) @ E2) @ F6))))))))))))).
% 3.45/1.76 thf(fact_93_prod__cases7, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,F5:$tType,G2:$tType,Y3:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F5) @ G2))))))]: ((~ ((! [A3:A,B4:B,C2:C,D2:D,E2:E,F6:F5,G3:G2]: ((Y3 != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F5) @ G2)))))) @ A3) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F5) @ G2))))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F5) @ G2)))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E) @ ((product_prod @ F5) @ G2))) @ D2) @ ((((product_Pair @ E) @ ((product_prod @ F5) @ G2)) @ E2) @ ((((product_Pair @ F5) @ G2) @ F6) @ G3)))))))))))))).
% 3.45/1.76 thf(fact_94_prod__induct3, axiom, (! [C:$tType,B:$tType,A:$tType,P3:(((product_prod @ A) @ ((product_prod @ B) @ C)) > $o),X7:((product_prod @ A) @ ((product_prod @ B) @ C))]: (((! [A3:A,B4:B,C2:C]: ((P3 @ ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A3) @ ((((product_Pair @ B) @ C) @ B4) @ C2))))) => (P3 @ X7))))).
% 3.45/1.76 thf(fact_95_prod__induct4, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,P3:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) > $o),X7:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D)))]: (((! [A3:A,B4:B,C2:C,D2:D]: ((P3 @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) @ A3) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D)) @ B4) @ ((((product_Pair @ C) @ D) @ C2) @ D2)))))) => (P3 @ X7))))).
% 3.45/1.76 thf(fact_96_prod__induct5, axiom, (! [E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P3:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) > $o),X7:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))))]: (((! [A3:A,B4:B,C2:C,D2:D,E2:E]: ((P3 @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) @ A3) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ E)) @ C2) @ ((((product_Pair @ D) @ E) @ D2) @ E2))))))) => (P3 @ X7))))).
% 3.45/1.76 thf(fact_97_prod__induct6, axiom, (! [F5:$tType,E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P3:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F5))))) > $o),X7:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F5)))))]: (((! [A3:A,B4:B,C2:C,D2:D,E2:E,F6:F5]: ((P3 @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F5))))) @ A3) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F5)))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F5))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E) @ F5)) @ D2) @ ((((product_Pair @ E) @ F5) @ E2) @ F6)))))))) => (P3 @ X7))))).
% 3.45/1.76 thf(fact_98_prod__induct7, axiom, (! [G2:$tType,F5:$tType,E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P3:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F5) @ G2)))))) > $o),X7:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F5) @ G2))))))]: (((! [A3:A,B4:B,C2:C,D2:D,E2:E,F6:F5,G3:G2]: ((P3 @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F5) @ G2)))))) @ A3) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F5) @ G2))))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F5) @ G2)))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E) @ ((product_prod @ F5) @ G2))) @ D2) @ ((((product_Pair @ E) @ ((product_prod @ F5) @ G2)) @ E2) @ ((((product_Pair @ F5) @ G2) @ F6) @ G3))))))))) => (P3 @ X7))))).
% 3.45/1.76 thf(fact_99_old_Oprod_Oexhaust, axiom, (! [A:$tType,B:$tType,Y3:((product_prod @ A) @ B)]: ((~ ((! [A3:A,B4:B]: ((Y3 != ((((product_Pair @ A) @ B) @ A3) @ B4))))))))).
% 3.45/1.76 thf(fact_100_old_Oprod_Oinducts, axiom, (! [B:$tType,A:$tType,P3:(((product_prod @ A) @ B) > $o),Prod:((product_prod @ A) @ B)]: (((! [A3:A,B4:B]: ((P3 @ ((((product_Pair @ A) @ B) @ A3) @ B4)))) => (P3 @ Prod))))).
% 3.45/1.76 thf(fact_101_old_Oprod_Orec, axiom, (! [A:$tType,T:$tType,B:$tType,F1:(A > (B > T)),A2:A,B2:B]: (((((((product_rec_prod @ A) @ B) @ T) @ F1) @ ((((product_Pair @ A) @ B) @ A2) @ B2)) = ((F1 @ A2) @ B2))))).
% 3.45/1.76 thf(fact_102_CH1_Oelims, axiom, (! [A:$tType,B:$tType,X7:(A > ((proces554692349s_term @ B) @ A)),Xa:((proces554692349s_term @ B) @ A),Y3:((proces554692349s_term @ B) @ A)]: (((((((proces1239275103le_CH1 @ A) @ B) @ X7) @ Xa) = Y3) => ((! [X4:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ B) @ X4)) => (Y3 != ((((((((proces460752237s_term @ A) @ ((proces554692349s_term @ B) @ A)) @ B) @ (^ [A5:A]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [P5:(proces634752977rocess @ B)]: ((((proces1062592052s_PROC @ B) @ A) @ ((proces979765041_ch1Of @ B) @ P5))))) @ (^ [A5:B,B5:((proces554692349s_term @ B) @ A)]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [T13:((proces554692349s_term @ B) @ A),T24:((proces554692349s_term @ B) @ A)]: (T13))) @ (X7 @ X4)))))) => ((! [P4:(proces634752977rocess @ B)]: (((Xa = (((proces1062592052s_PROC @ B) @ A) @ P4)) => (Y3 != (((proces1062592052s_PROC @ B) @ A) @ ((proces979765041_ch1Of @ B) @ P4)))))) => ((! [T12:((proces554692349s_term @ B) @ A)]: (((? [T23:((proces554692349s_term @ B) @ A)]: ((Xa = ((((proces89589571ess_CH @ B) @ A) @ T12) @ T23)))) => (Y3 != T12)))) => (~ (((? [V:B,Va:((proces554692349s_term @ B) @ A)]: ((Xa = ((((proces1454156180ss_ACT @ B) @ A) @ V) @ Va)))) => (Y3 != (undefined @ ((proces554692349s_term @ B) @ A))))))))))))).
% 3.45/1.76 thf(fact_103_CH2_Oelims, axiom, (! [A:$tType,B:$tType,X7:(A > ((proces554692349s_term @ B) @ A)),Xa:((proces554692349s_term @ B) @ A),Y3:((proces554692349s_term @ B) @ A)]: (((((((proces1239275104le_CH2 @ A) @ B) @ X7) @ Xa) = Y3) => ((! [X4:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ B) @ X4)) => (Y3 != ((((((((proces460752237s_term @ A) @ ((proces554692349s_term @ B) @ A)) @ B) @ (^ [A5:A]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [P5:(proces634752977rocess @ B)]: ((((proces1062592052s_PROC @ B) @ A) @ ((proces988026546_ch2Of @ B) @ P5))))) @ (^ [A5:B,B5:((proces554692349s_term @ B) @ A)]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [T13:((proces554692349s_term @ B) @ A),T24:((proces554692349s_term @ B) @ A)]: (T24))) @ (X7 @ X4)))))) => ((! [P4:(proces634752977rocess @ B)]: (((Xa = (((proces1062592052s_PROC @ B) @ A) @ P4)) => (Y3 != (((proces1062592052s_PROC @ B) @ A) @ ((proces988026546_ch2Of @ B) @ P4)))))) => ((! [T12:((proces554692349s_term @ B) @ A),T23:((proces554692349s_term @ B) @ A)]: (((Xa = ((((proces89589571ess_CH @ B) @ A) @ T12) @ T23)) => (Y3 != T23)))) => (~ (((? [V:B,Va:((proces554692349s_term @ B) @ A)]: ((Xa = ((((proces1454156180ss_ACT @ B) @ A) @ V) @ Va)))) => (Y3 != (undefined @ ((proces554692349s_term @ B) @ A))))))))))))).
% 3.45/1.76 thf(fact_104_CH1_Opelims, axiom, (! [A:$tType,B:$tType,X7:(A > ((proces554692349s_term @ B) @ A)),Xa:((proces554692349s_term @ B) @ A),Y3:((proces554692349s_term @ B) @ A)]: (((((((proces1239275103le_CH1 @ A) @ B) @ X7) @ Xa) = Y3) => ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces1869379930H1_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X7) @ Xa)) => ((! [X4:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ B) @ X4)) => ((Y3 = ((((((((proces460752237s_term @ A) @ ((proces554692349s_term @ B) @ A)) @ B) @ (^ [A5:A]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [P5:(proces634752977rocess @ B)]: ((((proces1062592052s_PROC @ B) @ A) @ ((proces979765041_ch1Of @ B) @ P5))))) @ (^ [A5:B,B5:((proces554692349s_term @ B) @ A)]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [T13:((proces554692349s_term @ B) @ A),T24:((proces554692349s_term @ B) @ A)]: (T13))) @ (X7 @ X4))) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces1869379930H1_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X7) @ (((proces1627516585ss_VAR @ A) @ B) @ X4))))))))) => ((! [P4:(proces634752977rocess @ B)]: (((Xa = (((proces1062592052s_PROC @ B) @ A) @ P4)) => ((Y3 = (((proces1062592052s_PROC @ B) @ A) @ ((proces979765041_ch1Of @ B) @ P4))) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces1869379930H1_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X7) @ (((proces1062592052s_PROC @ B) @ A) @ P4))))))))) => ((! [T12:((proces554692349s_term @ B) @ A),T23:((proces554692349s_term @ B) @ A)]: (((Xa = ((((proces89589571ess_CH @ B) @ A) @ T12) @ T23)) => ((Y3 = T12) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces1869379930H1_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X7) @ ((((proces89589571ess_CH @ B) @ A) @ T12) @ T23))))))))) => (~ ((! [V:B,Va:((proces554692349s_term @ B) @ A)]: (((Xa = ((((proces1454156180ss_ACT @ B) @ A) @ V) @ Va)) => ((Y3 = (undefined @ ((proces554692349s_term @ B) @ A))) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces1869379930H1_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X7) @ ((((proces1454156180ss_ACT @ B) @ A) @ V) @ Va))))))))))))))))))).
% 3.45/1.76 thf(fact_105_CH2_Opelims, axiom, (! [A:$tType,B:$tType,X7:(A > ((proces554692349s_term @ B) @ A)),Xa:((proces554692349s_term @ B) @ A),Y3:((proces554692349s_term @ B) @ A)]: (((((((proces1239275104le_CH2 @ A) @ B) @ X7) @ Xa) = Y3) => ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces93903513H2_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X7) @ Xa)) => ((! [X4:A]: (((Xa = (((proces1627516585ss_VAR @ A) @ B) @ X4)) => ((Y3 = ((((((((proces460752237s_term @ A) @ ((proces554692349s_term @ B) @ A)) @ B) @ (^ [A5:A]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [P5:(proces634752977rocess @ B)]: ((((proces1062592052s_PROC @ B) @ A) @ ((proces988026546_ch2Of @ B) @ P5))))) @ (^ [A5:B,B5:((proces554692349s_term @ B) @ A)]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [T13:((proces554692349s_term @ B) @ A),T24:((proces554692349s_term @ B) @ A)]: (T24))) @ (X7 @ X4))) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces93903513H2_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X7) @ (((proces1627516585ss_VAR @ A) @ B) @ X4))))))))) => ((! [P4:(proces634752977rocess @ B)]: (((Xa = (((proces1062592052s_PROC @ B) @ A) @ P4)) => ((Y3 = (((proces1062592052s_PROC @ B) @ A) @ ((proces988026546_ch2Of @ B) @ P4))) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces93903513H2_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X7) @ (((proces1062592052s_PROC @ B) @ A) @ P4))))))))) => ((! [T12:((proces554692349s_term @ B) @ A),T23:((proces554692349s_term @ B) @ A)]: (((Xa = ((((proces89589571ess_CH @ B) @ A) @ T12) @ T23)) => ((Y3 = T23) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces93903513H2_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X7) @ ((((proces89589571ess_CH @ B) @ A) @ T12) @ T23))))))))) => (~ ((! [V:B,Va:((proces554692349s_term @ B) @ A)]: (((Xa = ((((proces1454156180ss_ACT @ B) @ A) @ V) @ Va)) => ((Y3 = (undefined @ ((proces554692349s_term @ B) @ A))) => (~ ((((accp @ ((product_prod @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A))) @ ((proces93903513H2_rel @ A) @ B)) @ ((((product_Pair @ (A > ((proces554692349s_term @ B) @ A))) @ ((proces554692349s_term @ B) @ A)) @ X7) @ ((((proces1454156180ss_ACT @ B) @ A) @ V) @ Va))))))))))))))))))).
% 3.45/1.76 thf(fact_106_ch1Of__def, axiom, (! [A:$tType]: (((proces979765041_ch1Of @ A) = ((((proces1406508781rocess @ A) @ (proces634752977rocess @ A)) @ (^ [Uu2:A,Uv:(proces634752977rocess @ A)]: ((undefined @ (proces634752977rocess @ A))))) @ (^ [X21:(proces634752977rocess @ A),X222:(proces634752977rocess @ A)]: (X21))))))).
% 3.45/1.76 thf(fact_107_CH2_Osimps_I2_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),P:(proces634752977rocess @ B)]: ((((((proces1239275104le_CH2 @ A) @ B) @ Sys) @ (((proces1062592052s_PROC @ B) @ A) @ P)) = (((proces1062592052s_PROC @ B) @ A) @ ((proces988026546_ch2Of @ B) @ P)))))).
% 3.45/1.76 thf(fact_108_CH1_Osimps_I2_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),P:(proces634752977rocess @ B)]: ((((((proces1239275103le_CH1 @ A) @ B) @ Sys) @ (((proces1062592052s_PROC @ B) @ A) @ P)) = (((proces1062592052s_PROC @ B) @ A) @ ((proces979765041_ch1Of @ B) @ P)))))).
% 3.45/1.76 thf(fact_109_solution_Osimps_I6_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T2:((proces554692349s_term @ B) @ A)]: (((~ (((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ T2))) => (((proces988026546_ch2Of @ B) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ T2)) = ((((proces1652378886lution @ A) @ B) @ Sys) @ ((((proces1239275104le_CH2 @ A) @ B) @ Sys) @ T2))))))).
% 3.45/1.76 thf(fact_110_solution_Osimps_I5_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T2:((proces554692349s_term @ B) @ A)]: (((~ (((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ T2))) => (((proces979765041_ch1Of @ B) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ T2)) = ((((proces1652378886lution @ A) @ B) @ Sys) @ ((((proces1239275103le_CH1 @ A) @ B) @ Sys) @ T2))))))).
% 3.45/1.76 thf(fact_111_CH2_Osimps_I3_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T1:((proces554692349s_term @ B) @ A),T22:((proces554692349s_term @ B) @ A)]: ((((((proces1239275104le_CH2 @ A) @ B) @ Sys) @ ((((proces89589571ess_CH @ B) @ A) @ T1) @ T22)) = T22)))).
% 3.45/1.76 thf(fact_112_CH1_Osimps_I3_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T1:((proces554692349s_term @ B) @ A),T22:((proces554692349s_term @ B) @ A)]: ((((((proces1239275103le_CH1 @ A) @ B) @ Sys) @ ((((proces89589571ess_CH @ B) @ A) @ T1) @ T22)) = T1)))).
% 3.45/1.76 thf(fact_113_process_Ocase__eq__if, axiom, (! [B:$tType,A:$tType]: ((((proces1406508781rocess @ A) @ B) = (^ [F12:(A > ((proces634752977rocess @ A) > B)),F22:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > B)),Process2:(proces634752977rocess @ A)]: (((((if @ B) @ ((proces10484146Action @ A) @ Process2)) @ ((F12 @ ((proces745025900prefOf @ A) @ Process2)) @ ((proces1778668539contOf @ A) @ Process2))) @ ((F22 @ ((proces979765041_ch1Of @ A) @ Process2)) @ ((proces988026546_ch2Of @ A) @ Process2))))))))).
% 3.45/1.76 thf(fact_114_CH2_Osimps_I1_J, axiom, (! [B:$tType,A:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),X3:A]: ((((((proces1239275104le_CH2 @ A) @ B) @ Sys) @ (((proces1627516585ss_VAR @ A) @ B) @ X3)) = ((((((((proces460752237s_term @ A) @ ((proces554692349s_term @ B) @ A)) @ B) @ (^ [A5:A]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [P5:(proces634752977rocess @ B)]: ((((proces1062592052s_PROC @ B) @ A) @ ((proces988026546_ch2Of @ B) @ P5))))) @ (^ [A5:B,B5:((proces554692349s_term @ B) @ A)]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [T13:((proces554692349s_term @ B) @ A),T24:((proces554692349s_term @ B) @ A)]: (T24))) @ (Sys @ X3)))))).
% 3.45/1.76 thf(fact_115_CH1_Osimps_I1_J, axiom, (! [B:$tType,A:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),X3:A]: ((((((proces1239275103le_CH1 @ A) @ B) @ Sys) @ (((proces1627516585ss_VAR @ A) @ B) @ X3)) = ((((((((proces460752237s_term @ A) @ ((proces554692349s_term @ B) @ A)) @ B) @ (^ [A5:A]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [P5:(proces634752977rocess @ B)]: ((((proces1062592052s_PROC @ B) @ A) @ ((proces979765041_ch1Of @ B) @ P5))))) @ (^ [A5:B,B5:((proces554692349s_term @ B) @ A)]: ((undefined @ ((proces554692349s_term @ B) @ A))))) @ (^ [T13:((proces554692349s_term @ B) @ A),T24:((proces554692349s_term @ B) @ A)]: (T13))) @ (Sys @ X3)))))).
% 3.45/1.76 thf(fact_116_ch2Of__def, axiom, (! [A:$tType]: (((proces988026546_ch2Of @ A) = ((((proces1406508781rocess @ A) @ (proces634752977rocess @ A)) @ (^ [Uu2:A,Uv:(proces634752977rocess @ A)]: ((undefined @ (proces634752977rocess @ A))))) @ (^ [X21:(proces634752977rocess @ A),X222:(proces634752977rocess @ A)]: (X222))))))).
% 3.45/1.76 thf(fact_117_solution_Ocode, axiom, (! [B:$tType,A:$tType]: ((((proces1652378886lution @ A) @ B) = (^ [Sys3:(A > ((proces554692349s_term @ B) @ A)),T4:((proces554692349s_term @ B) @ A)]: (((((if @ (proces634752977rocess @ B)) @ ((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys3) @ T4)) @ (((proces1525233512Action @ B) @ (((((proces1708129104e_PREF @ A) @ B) @ A) @ Sys3) @ T4)) @ ((((proces1652378886lution @ A) @ B) @ Sys3) @ ((((proces126235999e_CONT @ A) @ B) @ Sys3) @ T4)))) @ (((proces1915862579Choice @ B) @ ((((proces1652378886lution @ A) @ B) @ Sys3) @ ((((proces1239275103le_CH1 @ A) @ B) @ Sys3) @ T4))) @ ((((proces1652378886lution @ A) @ B) @ Sys3) @ ((((proces1239275104le_CH2 @ A) @ B) @ Sys3) @ T4)))))))))).
% 3.45/1.76 thf(fact_118_process_Osplit__sel__asm, axiom, (! [B:$tType,A:$tType,P3:(B > $o),F1:(A > ((proces634752977rocess @ A) > B)),F2:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > B)),Process:(proces634752977rocess @ A)]: (((P3 @ (((((proces1406508781rocess @ A) @ B) @ F1) @ F2) @ Process)) = (~ ((((Process = (((proces1525233512Action @ A) @ ((proces745025900prefOf @ A) @ Process)) @ ((proces1778668539contOf @ A) @ Process))) & (~ ((P3 @ ((F1 @ ((proces745025900prefOf @ A) @ Process)) @ ((proces1778668539contOf @ A) @ Process)))))) | ((Process = (((proces1915862579Choice @ A) @ ((proces979765041_ch1Of @ A) @ Process)) @ ((proces988026546_ch2Of @ A) @ Process))) & (~ ((P3 @ ((F2 @ ((proces979765041_ch1Of @ A) @ Process)) @ ((proces988026546_ch2Of @ A) @ Process))))))))))))).
% 3.45/1.76 thf(fact_119_process_Osplit__sel, axiom, (! [B:$tType,A:$tType,P3:(B > $o),F1:(A > ((proces634752977rocess @ A) > B)),F2:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > B)),Process:(proces634752977rocess @ A)]: (((P3 @ (((((proces1406508781rocess @ A) @ B) @ F1) @ F2) @ Process)) = (((Process = (((proces1525233512Action @ A) @ ((proces745025900prefOf @ A) @ Process)) @ ((proces1778668539contOf @ A) @ Process))) => (P3 @ ((F1 @ ((proces745025900prefOf @ A) @ Process)) @ ((proces1778668539contOf @ A) @ Process)))) & ((Process = (((proces1915862579Choice @ A) @ ((proces979765041_ch1Of @ A) @ Process)) @ ((proces988026546_ch2Of @ A) @ Process))) => (P3 @ ((F2 @ ((proces979765041_ch1Of @ A) @ Process)) @ ((proces988026546_ch2Of @ A) @ Process))))))))).
% 3.45/1.76 thf(fact_120_process_Oexpand, axiom, (! [A:$tType,Process:(proces634752977rocess @ A),Process3:(proces634752977rocess @ A)]: (((((proces10484146Action @ A) @ Process) = ((proces10484146Action @ A) @ Process3)) => ((((proces10484146Action @ A) @ Process) => (((proces10484146Action @ A) @ Process3) => ((((proces745025900prefOf @ A) @ Process) = ((proces745025900prefOf @ A) @ Process3)) & (((proces1778668539contOf @ A) @ Process) = ((proces1778668539contOf @ A) @ Process3))))) => ((((proces401113213Choice @ A) @ Process) => (((proces401113213Choice @ A) @ Process3) => ((((proces979765041_ch1Of @ A) @ Process) = ((proces979765041_ch1Of @ A) @ Process3)) & (((proces988026546_ch2Of @ A) @ Process) = ((proces988026546_ch2Of @ A) @ Process3))))) => (Process = Process3))))))).
% 3.45/1.76 thf(fact_121_process_Ocoinduct, axiom, (! [A:$tType,R:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > $o)),Process:(proces634752977rocess @ A),Process3:(proces634752977rocess @ A)]: ((((R @ Process) @ Process3) => ((! [Process4:(proces634752977rocess @ A),Process5:(proces634752977rocess @ A)]: ((((R @ Process4) @ Process5) => ((((proces10484146Action @ A) @ Process4) = ((proces10484146Action @ A) @ Process5)) & ((((proces10484146Action @ A) @ Process4) => (((proces10484146Action @ A) @ Process5) => ((((proces745025900prefOf @ A) @ Process4) = ((proces745025900prefOf @ A) @ Process5)) & ((R @ ((proces1778668539contOf @ A) @ Process4)) @ ((proces1778668539contOf @ A) @ Process5))))) & (((proces401113213Choice @ A) @ Process4) => (((proces401113213Choice @ A) @ Process5) => (((R @ ((proces979765041_ch1Of @ A) @ Process4)) @ ((proces979765041_ch1Of @ A) @ Process5)) & ((R @ ((proces988026546_ch2Of @ A) @ Process4)) @ ((proces988026546_ch2Of @ A) @ Process5)))))))))) => (Process = Process3)))))).
% 3.45/1.76 thf(fact_122_process_Oinject_I2_J, axiom, (! [A:$tType,X212:(proces634752977rocess @ A),X223:(proces634752977rocess @ A),Y21:(proces634752977rocess @ A),Y22:(proces634752977rocess @ A)]: ((((((proces1915862579Choice @ A) @ X212) @ X223) = (((proces1915862579Choice @ A) @ Y21) @ Y22)) = ((X212 = Y21) & (X223 = Y22)))))).
% 3.45/1.76 thf(fact_123_process_Opred__inject_I2_J, axiom, (! [A:$tType,P3:(A > $o),A2:(proces634752977rocess @ A),Aa2:(proces634752977rocess @ A)]: (((((proces1205983068rocess @ A) @ P3) @ (((proces1915862579Choice @ A) @ A2) @ Aa2)) = ((((proces1205983068rocess @ A) @ P3) @ A2) & (((proces1205983068rocess @ A) @ P3) @ Aa2)))))).
% 3.45/1.76 thf(fact_124_solution_Odisc__iff_I2_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T2:((proces554692349s_term @ B) @ A)]: ((((proces401113213Choice @ B) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ T2)) = (~ (((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ T2))))))).
% 3.45/1.76 thf(fact_125_process_Ocollapse_I2_J, axiom, (! [A:$tType,Process:(proces634752977rocess @ A)]: ((((proces401113213Choice @ A) @ Process) => ((((proces1915862579Choice @ A) @ ((proces979765041_ch1Of @ A) @ Process)) @ ((proces988026546_ch2Of @ A) @ Process)) = Process))))).
% 3.45/1.76 thf(fact_126_process_Odisc_I4_J, axiom, (! [A:$tType,X212:(proces634752977rocess @ A),X223:(proces634752977rocess @ A)]: (((proces401113213Choice @ A) @ (((proces1915862579Choice @ A) @ X212) @ X223))))).
% 3.45/1.76 thf(fact_127_process_OdiscI_I2_J, axiom, (! [A:$tType,Process:(proces634752977rocess @ A),X212:(proces634752977rocess @ A),X223:(proces634752977rocess @ A)]: (((Process = (((proces1915862579Choice @ A) @ X212) @ X223)) => ((proces401113213Choice @ A) @ Process))))).
% 3.45/1.76 thf(fact_128_isChoice__def, axiom, (! [A:$tType]: (((proces401113213Choice @ A) = (^ [Process2:(proces634752977rocess @ A)]: ((? [X21:(proces634752977rocess @ A),X222:(proces634752977rocess @ A)]: ((Process2 = (((proces1915862579Choice @ A) @ X21) @ X222)))))))))).
% 3.45/1.76 thf(fact_129_process__strong__coind, axiom, (! [A:$tType,Phi:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > $o)),P:(proces634752977rocess @ A),P6:(proces634752977rocess @ A)]: ((((Phi @ P) @ P6) => ((! [P4:(proces634752977rocess @ A),P7:(proces634752977rocess @ A)]: ((((Phi @ P4) @ P7) => ((((proces10484146Action @ A) @ P4) = ((proces10484146Action @ A) @ P7)) & (((proces401113213Choice @ A) @ P4) = ((proces401113213Choice @ A) @ P7)))))) => ((! [A3:A,A7:A,P4:(proces634752977rocess @ A),P7:(proces634752977rocess @ A)]: ((((Phi @ (((proces1525233512Action @ A) @ A3) @ P4)) @ (((proces1525233512Action @ A) @ A7) @ P7)) => ((A3 = A7) & (((Phi @ P4) @ P7) | (P4 = P7)))))) => ((! [P4:(proces634752977rocess @ A),Q2:(proces634752977rocess @ A),P7:(proces634752977rocess @ A),Q3:(proces634752977rocess @ A)]: ((((Phi @ (((proces1915862579Choice @ A) @ P4) @ Q2)) @ (((proces1915862579Choice @ A) @ P7) @ Q3)) => ((((Phi @ P4) @ P7) | (P4 = P7)) & (((Phi @ Q2) @ Q3) | (Q2 = Q3)))))) => (P = P6)))))))).
% 3.45/1.76 thf(fact_130_process__coind, axiom, (! [A:$tType,Phi:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > $o)),P:(proces634752977rocess @ A),P6:(proces634752977rocess @ A)]: ((((Phi @ P) @ P6) => ((! [P4:(proces634752977rocess @ A),P7:(proces634752977rocess @ A)]: ((((Phi @ P4) @ P7) => ((((proces10484146Action @ A) @ P4) = ((proces10484146Action @ A) @ P7)) & (((proces401113213Choice @ A) @ P4) = ((proces401113213Choice @ A) @ P7)))))) => ((! [A3:A,A7:A,P4:(proces634752977rocess @ A),P7:(proces634752977rocess @ A)]: ((((Phi @ (((proces1525233512Action @ A) @ A3) @ P4)) @ (((proces1525233512Action @ A) @ A7) @ P7)) => ((A3 = A7) & ((Phi @ P4) @ P7))))) => ((! [P4:(proces634752977rocess @ A),Q2:(proces634752977rocess @ A),P7:(proces634752977rocess @ A),Q3:(proces634752977rocess @ A)]: ((((Phi @ (((proces1915862579Choice @ A) @ P4) @ Q2)) @ (((proces1915862579Choice @ A) @ P7) @ Q3)) => (((Phi @ P4) @ P7) & ((Phi @ Q2) @ Q3))))) => (P = P6)))))))).
% 3.45/1.76 thf(fact_131_process_Odisc_I2_J, axiom, (! [A:$tType,X212:(proces634752977rocess @ A),X223:(proces634752977rocess @ A)]: ((~ (((proces10484146Action @ A) @ (((proces1915862579Choice @ A) @ X212) @ X223))))))).
% 3.45/1.76 thf(fact_132_process_Odistinct_I1_J, axiom, (! [A:$tType,X11:A,X122:(proces634752977rocess @ A),X212:(proces634752977rocess @ A),X223:(proces634752977rocess @ A)]: (((((proces1525233512Action @ A) @ X11) @ X122) != (((proces1915862579Choice @ A) @ X212) @ X223))))).
% 3.45/1.76 thf(fact_133_process_Oexhaust, axiom, (! [A:$tType,Y3:(proces634752977rocess @ A)]: (((! [X113:A,X124:(proces634752977rocess @ A)]: ((Y3 != (((proces1525233512Action @ A) @ X113) @ X124)))) => (~ ((! [X213:(proces634752977rocess @ A),X224:(proces634752977rocess @ A)]: ((Y3 != (((proces1915862579Choice @ A) @ X213) @ X224)))))))))).
% 3.45/1.76 thf(fact_134_process_Osel_I4_J, axiom, (! [A:$tType,X212:(proces634752977rocess @ A),X223:(proces634752977rocess @ A)]: ((((proces988026546_ch2Of @ A) @ (((proces1915862579Choice @ A) @ X212) @ X223)) = X223)))).
% 3.45/1.76 thf(fact_135_process_Osel_I3_J, axiom, (! [A:$tType,X212:(proces634752977rocess @ A),X223:(proces634752977rocess @ A)]: ((((proces979765041_ch1Of @ A) @ (((proces1915862579Choice @ A) @ X212) @ X223)) = X212)))).
% 3.45/1.76 thf(fact_136_process_Odistinct__disc_I2_J, axiom, (! [A:$tType,Process:(proces634752977rocess @ A)]: ((((proces401113213Choice @ A) @ Process) => (~ (((proces10484146Action @ A) @ Process))))))).
% 3.45/1.76 thf(fact_137_process_Odistinct__disc_I1_J, axiom, (! [A:$tType,Process:(proces634752977rocess @ A)]: ((((proces10484146Action @ A) @ Process) => (~ (((proces401113213Choice @ A) @ Process))))))).
% 3.45/1.76 thf(fact_138_isAction__isChoice, axiom, (! [A:$tType,P:(proces634752977rocess @ A)]: ((((proces10484146Action @ A) @ P) | ((proces401113213Choice @ A) @ P))))).
% 3.45/1.76 thf(fact_139_process_Oexhaust__disc, axiom, (! [A:$tType,Process:(proces634752977rocess @ A)]: (((~ (((proces10484146Action @ A) @ Process))) => ((proces401113213Choice @ A) @ Process))))).
% 3.45/1.76 thf(fact_140_not__isAction__isChoice, axiom, (! [A:$tType,P:(proces634752977rocess @ A)]: ((~ ((((proces10484146Action @ A) @ P) & ((proces401113213Choice @ A) @ P))))))).
% 3.45/1.76 thf(fact_141_process_Odisc_I3_J, axiom, (! [A:$tType,X11:A,X122:(proces634752977rocess @ A)]: ((~ (((proces401113213Choice @ A) @ (((proces1525233512Action @ A) @ X11) @ X122))))))).
% 3.45/1.76 thf(fact_142_process_Osimps_I6_J, axiom, (! [B:$tType,A:$tType,F1:(A > ((proces634752977rocess @ A) > B)),F2:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > B)),X212:(proces634752977rocess @ A),X223:(proces634752977rocess @ A)]: (((((((proces1406508781rocess @ A) @ B) @ F1) @ F2) @ (((proces1915862579Choice @ A) @ X212) @ X223)) = ((F2 @ X212) @ X223))))).
% 3.45/1.76 thf(fact_143_solution_Odisc_I2_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T2:((proces554692349s_term @ B) @ A)]: (((~ (((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ T2))) => ((proces401113213Choice @ B) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ T2)))))).
% 3.45/1.76 thf(fact_144_process_Odisc__eq__case_I2_J, axiom, (! [A:$tType]: (((proces401113213Choice @ A) = ((((proces1406508781rocess @ A) @ $o) @ (^ [Uu:A,Uv2:(proces634752977rocess @ A)]: ($false))) @ (^ [Uu:(proces634752977rocess @ A),Uv2:(proces634752977rocess @ A)]: ($true))))))).
% 3.45/1.76 thf(fact_145_solution_Octr_I2_J, axiom, (! [A:$tType,B:$tType,Sys:(A > ((proces554692349s_term @ B) @ A)),T2:((proces554692349s_term @ B) @ A)]: (((~ (((((((proces687458811_isACT @ A) @ B) @ A) @ B) @ Sys) @ T2))) => (((((proces1652378886lution @ A) @ B) @ Sys) @ T2) = (((proces1915862579Choice @ B) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ ((((proces1239275103le_CH1 @ A) @ B) @ Sys) @ T2))) @ ((((proces1652378886lution @ A) @ B) @ Sys) @ ((((proces1239275104le_CH2 @ A) @ B) @ Sys) @ T2)))))))).
% 3.45/1.76 thf(fact_146_process_Oexhaust__sel, axiom, (! [A:$tType,Process:(proces634752977rocess @ A)]: (((Process != (((proces1525233512Action @ A) @ ((proces745025900prefOf @ A) @ Process)) @ ((proces1778668539contOf @ A) @ Process))) => (Process = (((proces1915862579Choice @ A) @ ((proces979765041_ch1Of @ A) @ Process)) @ ((proces988026546_ch2Of @ A) @ Process))))))).
% 3.45/1.76 thf(fact_147_process_Ocoinduct__strong, axiom, (! [A:$tType,R:((proces634752977rocess @ A) > ((proces634752977rocess @ A) > $o)),Process:(proces634752977rocess @ A),Process3:(proces634752977rocess @ A)]: ((((R @ Process) @ Process3) => ((! [Process4:(proces634752977rocess @ A),Process5:(proces634752977rocess @ A)]: ((((R @ Process4) @ Process5) => ((((proces10484146Action @ A) @ Process4) = ((proces10484146Action @ A) @ Process5)) & ((((proces10484146Action @ A) @ Process4) => (((proces10484146Action @ A) @ Process5) => ((((proces745025900prefOf @ A) @ Process4) = ((proces745025900prefOf @ A) @ Process5)) & (((R @ ((proces1778668539contOf @ A) @ Process4)) @ ((proces1778668539contOf @ A) @ Process5)) | (((proces1778668539contOf @ A) @ Process4) = ((proces1778668539contOf @ A) @ Process5)))))) & (((proces401113213Choice @ A) @ Process4) => (((proces401113213Choice @ A) @ Process5) => ((((R @ ((proces979765041_ch1Of @ A) @ Process4)) @ ((proces979765041_ch1Of @ A) @ Process5)) | (((proces979765041_ch1Of @ A) @ Process4) = ((proces979765041_ch1Of @ A) @ Process5))) & (((R @ ((proces988026546_ch2Of @ A) @ Process4)) @ ((proces988026546_ch2Of @ A) @ Process5)) | (((proces988026546_ch2Of @ A) @ Process4) = ((proces988026546_ch2Of @ A) @ Process5))))))))))) => (Process = Process3)))))).
% 3.45/1.76 thf(fact_148_process_Orel__sel, axiom, (! [B:$tType,A:$tType]: ((((proces749077512rocess @ A) @ B) = (^ [R2:(A > (B > $o)),A5:(proces634752977rocess @ A),B5:(proces634752977rocess @ B)]: (((((proces10484146Action @ A) @ A5) = ((proces10484146Action @ B) @ B5)) & ((((proces10484146Action @ A) @ A5) => (((proces10484146Action @ B) @ B5) => (((R2 @ ((proces745025900prefOf @ A) @ A5)) @ ((proces745025900prefOf @ B) @ B5)) & (((((proces749077512rocess @ A) @ B) @ R2) @ ((proces1778668539contOf @ A) @ A5)) @ ((proces1778668539contOf @ B) @ B5))))) & (((proces401113213Choice @ A) @ A5) => (((proces401113213Choice @ B) @ B5) => ((((((proces749077512rocess @ A) @ B) @ R2) @ ((proces979765041_ch1Of @ A) @ A5)) @ ((proces979765041_ch1Of @ B) @ B5)) & (((((proces749077512rocess @ A) @ B) @ R2) @ ((proces988026546_ch2Of @ A) @ A5)) @ ((proces988026546_ch2Of @ B) @ B5))))))))))))).
% 3.45/1.76 thf(fact_149_process_Orel__coinduct, axiom, (! [A:$tType,B:$tType,P3:((proces634752977rocess @ A) > ((proces634752977rocess @ B) > $o)),X7:(proces634752977rocess @ A),Y3:(proces634752977rocess @ B),R:(A > (B > $o))]: ((((P3 @ X7) @ Y3) => ((! [Process4:(proces634752977rocess @ A),Process5:(proces634752977rocess @ B)]: ((((P3 @ Process4) @ Process5) => ((((proces10484146Action @ A) @ Process4) = ((proces10484146Action @ B) @ Process5)) & ((((proces10484146Action @ A) @ Process4) => (((proces10484146Action @ B) @ Process5) => (((R @ ((proces745025900prefOf @ A) @ Process4)) @ ((proces745025900prefOf @ B) @ Process5)) & ((P3 @ ((proces1778668539contOf @ A) @ Process4)) @ ((proces1778668539contOf @ B) @ Process5))))) & (((proces401113213Choice @ A) @ Process4) => (((proces401113213Choice @ B) @ Process5) => (((P3 @ ((proces979765041_ch1Of @ A) @ Process4)) @ ((proces979765041_ch1Of @ B) @ Process5)) & ((P3 @ ((proces988026546_ch2Of @ A) @ Process4)) @ ((proces988026546_ch2Of @ B) @ Process5)))))))))) => (((((proces749077512rocess @ A) @ B) @ R) @ X7) @ Y3)))))).
% 3.45/1.76 thf(fact_150_pred__equals__eq2, axiom, (! [B:$tType,A:$tType,R:(set @ ((product_prod @ A) @ B)),S:(set @ ((product_prod @ A) @ B))]: ((((^ [X:A,Y5:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X) @ Y5)) @ R))) = (^ [X:A,Y5:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X) @ Y5)) @ S)))) = (R = S))))).
% 3.45/1.76 thf(fact_151_internal__case__prod__conv, axiom, (! [B:$tType,A:$tType,C:$tType,C3:(B > (C > A)),A2:B,B2:C]: (((((((produc2004651681e_prod @ B) @ C) @ A) @ C3) @ ((((product_Pair @ B) @ C) @ A2) @ B2)) = ((C3 @ A2) @ B2))))).
% 3.45/1.76 thf(fact_152_process_Orel__inject_I1_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X11:A,X122:(proces634752977rocess @ A),Y11:B,Y12:(proces634752977rocess @ B)]: (((((((proces749077512rocess @ A) @ B) @ R) @ (((proces1525233512Action @ A) @ X11) @ X122)) @ (((proces1525233512Action @ B) @ Y11) @ Y12)) = (((R @ X11) @ Y11) & (((((proces749077512rocess @ A) @ B) @ R) @ X122) @ Y12)))))).
% 3.45/1.76 thf(fact_153_process_Orel__inject_I2_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X212:(proces634752977rocess @ A),X223:(proces634752977rocess @ A),Y21:(proces634752977rocess @ B),Y22:(proces634752977rocess @ B)]: (((((((proces749077512rocess @ A) @ B) @ R) @ (((proces1915862579Choice @ A) @ X212) @ X223)) @ (((proces1915862579Choice @ B) @ Y21) @ Y22)) = ((((((proces749077512rocess @ A) @ B) @ R) @ X212) @ Y21) & (((((proces749077512rocess @ A) @ B) @ R) @ X223) @ Y22)))))).
% 3.45/1.76 thf(fact_154_process_Orel__intros_I2_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X212:(proces634752977rocess @ A),Y21:(proces634752977rocess @ B),X223:(proces634752977rocess @ A),Y22:(proces634752977rocess @ B)]: (((((((proces749077512rocess @ A) @ B) @ R) @ X212) @ Y21) => ((((((proces749077512rocess @ A) @ B) @ R) @ X223) @ Y22) => (((((proces749077512rocess @ A) @ B) @ R) @ (((proces1915862579Choice @ A) @ X212) @ X223)) @ (((proces1915862579Choice @ B) @ Y21) @ Y22))))))).
% 3.45/1.76 thf(fact_155_process_Orel__refl, axiom, (! [B:$tType,Ra:(B > (B > $o)),X7:(proces634752977rocess @ B)]: (((! [X6:B]: (((Ra @ X6) @ X6))) => (((((proces749077512rocess @ B) @ B) @ Ra) @ X7) @ X7))))).
% 3.45/1.76 thf(fact_156_process_Orel__eq, axiom, (! [A:$tType]: (((((proces749077512rocess @ A) @ A) @ (^ [Y6:A,Z:A]: ((Y6 = Z)))) = (^ [Y6:(proces634752977rocess @ A),Z:(proces634752977rocess @ A)]: ((Y6 = Z))))))).
% 3.45/1.76 thf(fact_157_process_Orel__intros_I1_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X11:A,Y11:B,X122:(proces634752977rocess @ A),Y12:(proces634752977rocess @ B)]: ((((R @ X11) @ Y11) => ((((((proces749077512rocess @ A) @ B) @ R) @ X122) @ Y12) => (((((proces749077512rocess @ A) @ B) @ R) @ (((proces1525233512Action @ A) @ X11) @ X122)) @ (((proces1525233512Action @ B) @ Y11) @ Y12))))))).
% 3.45/1.76 thf(fact_158_process_Orel__distinct_I2_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),Y21:(proces634752977rocess @ A),Y22:(proces634752977rocess @ A),X11:B,X122:(proces634752977rocess @ B)]: ((~ ((((((proces749077512rocess @ A) @ B) @ R) @ (((proces1915862579Choice @ A) @ Y21) @ Y22)) @ (((proces1525233512Action @ B) @ X11) @ X122))))))).
% 3.45/1.76 thf(fact_159_process_Orel__distinct_I1_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X11:A,X122:(proces634752977rocess @ A),Y21:(proces634752977rocess @ B),Y22:(proces634752977rocess @ B)]: ((~ ((((((proces749077512rocess @ A) @ B) @ R) @ (((proces1525233512Action @ A) @ X11) @ X122)) @ (((proces1915862579Choice @ B) @ Y21) @ Y22))))))).
% 3.45/1.76 thf(fact_160_process_Orel__cases, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),A2:(proces634752977rocess @ A),B2:(proces634752977rocess @ B)]: (((((((proces749077512rocess @ A) @ B) @ R) @ A2) @ B2) => ((! [X13:A,X23:(proces634752977rocess @ A)]: (((A2 = (((proces1525233512Action @ A) @ X13) @ X23)) => (! [Y13:B,Y23:(proces634752977rocess @ B)]: (((B2 = (((proces1525233512Action @ B) @ Y13) @ Y23)) => (((R @ X13) @ Y13) => (~ ((((((proces749077512rocess @ A) @ B) @ R) @ X23) @ Y23)))))))))) => (~ ((! [X1a:(proces634752977rocess @ A),X2a:(proces634752977rocess @ A)]: (((A2 = (((proces1915862579Choice @ A) @ X1a) @ X2a)) => (! [Y1a:(proces634752977rocess @ B),Y2a:(proces634752977rocess @ B)]: (((B2 = (((proces1915862579Choice @ B) @ Y1a) @ Y2a)) => ((((((proces749077512rocess @ A) @ B) @ R) @ X1a) @ Y1a) => (~ ((((((proces749077512rocess @ A) @ B) @ R) @ X2a) @ Y2a))))))))))))))))).
% 3.45/1.76 thf(fact_161_process__term_Orel__induct, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X7:((proces554692349s_term @ A) @ Pvar),Y3:((proces554692349s_term @ B) @ C),Q:(((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ B) @ C) > $o))]: ((((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ X7) @ Y3) => ((! [A12:Pvar,B1:C]: ((((R22 @ A12) @ B1) => ((Q @ (((proces1627516585ss_VAR @ Pvar) @ A) @ A12)) @ (((proces1627516585ss_VAR @ C) @ B) @ B1))))) => ((! [A22:(proces634752977rocess @ A),B22:(proces634752977rocess @ B)]: (((((((proces749077512rocess @ A) @ B) @ R1) @ A22) @ B22) => ((Q @ (((proces1062592052s_PROC @ A) @ Pvar) @ A22)) @ (((proces1062592052s_PROC @ B) @ C) @ B22))))) => ((! [A31:A,A32:((proces554692349s_term @ A) @ Pvar),B31:B,B32:((proces554692349s_term @ B) @ C)]: ((((R1 @ A31) @ B31) => (((Q @ A32) @ B32) => ((Q @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ A31) @ A32)) @ ((((proces1454156180ss_ACT @ B) @ C) @ B31) @ B32)))))) => ((! [A41:((proces554692349s_term @ A) @ Pvar),A42:((proces554692349s_term @ A) @ Pvar),B41:((proces554692349s_term @ B) @ C),B42:((proces554692349s_term @ B) @ C)]: ((((Q @ A41) @ B41) => (((Q @ A42) @ B42) => ((Q @ ((((proces89589571ess_CH @ A) @ Pvar) @ A41) @ A42)) @ ((((proces89589571ess_CH @ B) @ C) @ B41) @ B42)))))) => ((Q @ X7) @ Y3))))))))).
% 3.45/1.76 thf(fact_162_process__term_Orel__cases, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),A2:((proces554692349s_term @ A) @ Pvar),B2:((proces554692349s_term @ B) @ C)]: ((((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ A2) @ B2) => ((! [X6:Pvar]: (((A2 = (((proces1627516585ss_VAR @ Pvar) @ A) @ X6)) => (! [Y4:C]: (((B2 = (((proces1627516585ss_VAR @ C) @ B) @ Y4)) => (~ (((R22 @ X6) @ Y4))))))))) => ((! [Xa2:(proces634752977rocess @ A)]: (((A2 = (((proces1062592052s_PROC @ A) @ Pvar) @ Xa2)) => (! [Ya:(proces634752977rocess @ B)]: (((B2 = (((proces1062592052s_PROC @ B) @ C) @ Ya)) => (~ ((((((proces749077512rocess @ A) @ B) @ R1) @ Xa2) @ Ya))))))))) => ((! [X1a:A,X2a:((proces554692349s_term @ A) @ Pvar)]: (((A2 = ((((proces1454156180ss_ACT @ A) @ Pvar) @ X1a) @ X2a)) => (! [Y1a:B,Y2a:((proces554692349s_term @ B) @ C)]: (((B2 = ((((proces1454156180ss_ACT @ B) @ C) @ Y1a) @ Y2a)) => (((R1 @ X1a) @ Y1a) => (~ (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ X2a) @ Y2a)))))))))) => (~ ((! [X1b:((proces554692349s_term @ A) @ Pvar),X2b:((proces554692349s_term @ A) @ Pvar)]: (((A2 = ((((proces89589571ess_CH @ A) @ Pvar) @ X1b) @ X2b)) => (! [Y1b:((proces554692349s_term @ B) @ C),Y2b:((proces554692349s_term @ B) @ C)]: (((B2 = ((((proces89589571ess_CH @ B) @ C) @ Y1b) @ Y2b)) => (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ X1b) @ Y1b) => (~ (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ X2b) @ Y2b))))))))))))))))))).
% 3.45/1.76 thf(fact_163_process__term_Oset__cases_I2_J, axiom, (! [Pvar:$tType,A:$tType,E3:Pvar,A2:((proces554692349s_term @ A) @ Pvar)]: (((((member @ Pvar) @ E3) @ (((proces1493547885s_term @ A) @ Pvar) @ A2)) => ((A2 != (((proces1627516585ss_VAR @ Pvar) @ A) @ E3)) => ((! [Z1:A,Z2:((proces554692349s_term @ A) @ Pvar)]: (((A2 = ((((proces1454156180ss_ACT @ A) @ Pvar) @ Z1) @ Z2)) => (~ ((((member @ Pvar) @ E3) @ (((proces1493547885s_term @ A) @ Pvar) @ Z2))))))) => ((! [Z1:((proces554692349s_term @ A) @ Pvar)]: (((? [Z2:((proces554692349s_term @ A) @ Pvar)]: ((A2 = ((((proces89589571ess_CH @ A) @ Pvar) @ Z1) @ Z2)))) => (~ ((((member @ Pvar) @ E3) @ (((proces1493547885s_term @ A) @ Pvar) @ Z1))))))) => (~ ((! [Z1:((proces554692349s_term @ A) @ Pvar),Z2:((proces554692349s_term @ A) @ Pvar)]: (((A2 = ((((proces89589571ess_CH @ A) @ Pvar) @ Z1) @ Z2)) => (~ ((((member @ Pvar) @ E3) @ (((proces1493547885s_term @ A) @ Pvar) @ Z2)))))))))))))))).
% 3.45/1.76 thf(fact_164_process__term_Oset__intros_I6_J, axiom, (! [A:$tType,Pvar:$tType,Ab2:Pvar]: ((((member @ Pvar) @ Ab2) @ (((proces1493547885s_term @ A) @ Pvar) @ (((proces1627516585ss_VAR @ Pvar) @ A) @ Ab2)))))).
% 3.45/1.76 thf(fact_165_process__term_Oset__intros_I8_J, axiom, (! [Pvar:$tType,A:$tType,Xk:Pvar,A1c:((proces554692349s_term @ A) @ Pvar),A2c:((proces554692349s_term @ A) @ Pvar)]: (((((member @ Pvar) @ Xk) @ (((proces1493547885s_term @ A) @ Pvar) @ A1c)) => (((member @ Pvar) @ Xk) @ (((proces1493547885s_term @ A) @ Pvar) @ ((((proces89589571ess_CH @ A) @ Pvar) @ A1c) @ A2c))))))).
% 3.45/1.76 thf(fact_166_process__term_Oset__intros_I9_J, axiom, (! [Pvar:$tType,A:$tType,Xm:Pvar,A2c:((proces554692349s_term @ A) @ Pvar),A1c:((proces554692349s_term @ A) @ Pvar)]: (((((member @ Pvar) @ Xm) @ (((proces1493547885s_term @ A) @ Pvar) @ A2c)) => (((member @ Pvar) @ Xm) @ (((proces1493547885s_term @ A) @ Pvar) @ ((((proces89589571ess_CH @ A) @ Pvar) @ A1c) @ A2c))))))).
% 3.45/1.76 thf(fact_167_process__term_Oset__intros_I7_J, axiom, (! [Pvar:$tType,A:$tType,Xi:Pvar,A2b:((proces554692349s_term @ A) @ Pvar),A1b:A]: (((((member @ Pvar) @ Xi) @ (((proces1493547885s_term @ A) @ Pvar) @ A2b)) => (((member @ Pvar) @ Xi) @ (((proces1493547885s_term @ A) @ Pvar) @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ A1b) @ A2b))))))).
% 3.45/1.76 thf(fact_168_process__term_Osimps_I51_J, axiom, (! [Pvar:$tType,A:$tType,X31:A,X32:((proces554692349s_term @ A) @ Pvar)]: (((((proces1493547885s_term @ A) @ Pvar) @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ X31) @ X32)) = (((proces1493547885s_term @ A) @ Pvar) @ X32))))).
% 3.45/1.76 thf(fact_169_process__term_Orel__intros_I1_J, axiom, (! [Pvar:$tType,A:$tType,B:$tType,C:$tType,R22:(Pvar > (C > $o)),X1:Pvar,Y1:C,R1:(A > (B > $o))]: ((((R22 @ X1) @ Y1) => ((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ (((proces1627516585ss_VAR @ Pvar) @ A) @ X1)) @ (((proces1627516585ss_VAR @ C) @ B) @ Y1)))))).
% 3.45/1.76 thf(fact_170_process__term_Orel__inject_I1_J, axiom, (! [B:$tType,A:$tType,Pvar:$tType,C:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X1:Pvar,Y1:C]: ((((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ (((proces1627516585ss_VAR @ Pvar) @ A) @ X1)) @ (((proces1627516585ss_VAR @ C) @ B) @ Y1)) = ((R22 @ X1) @ Y1))))).
% 3.45/1.76 thf(fact_171_process__term_Orel__intros_I4_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X41:((proces554692349s_term @ A) @ Pvar),Y41:((proces554692349s_term @ B) @ C),X42:((proces554692349s_term @ A) @ Pvar),Y42:((proces554692349s_term @ B) @ C)]: ((((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ X41) @ Y41) => (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ X42) @ Y42) => ((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ ((((proces89589571ess_CH @ A) @ Pvar) @ X41) @ X42)) @ ((((proces89589571ess_CH @ B) @ C) @ Y41) @ Y42))))))).
% 3.45/1.76 thf(fact_172_process__term_Orel__inject_I4_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X41:((proces554692349s_term @ A) @ Pvar),X42:((proces554692349s_term @ A) @ Pvar),Y41:((proces554692349s_term @ B) @ C),Y42:((proces554692349s_term @ B) @ C)]: ((((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ ((((proces89589571ess_CH @ A) @ Pvar) @ X41) @ X42)) @ ((((proces89589571ess_CH @ B) @ C) @ Y41) @ Y42)) = (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ X41) @ Y41) & ((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ X42) @ Y42)))))).
% 3.45/1.76 thf(fact_173_process__term_Orel__intros_I3_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),X31:A,Y31:B,R22:(Pvar > (C > $o)),X32:((proces554692349s_term @ A) @ Pvar),Y32:((proces554692349s_term @ B) @ C)]: ((((R1 @ X31) @ Y31) => (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ X32) @ Y32) => ((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ X31) @ X32)) @ ((((proces1454156180ss_ACT @ B) @ C) @ Y31) @ Y32))))))).
% 3.45/1.76 thf(fact_174_process__term_Orel__inject_I3_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X31:A,X32:((proces554692349s_term @ A) @ Pvar),Y31:B,Y32:((proces554692349s_term @ B) @ C)]: ((((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ X31) @ X32)) @ ((((proces1454156180ss_ACT @ B) @ C) @ Y31) @ Y32)) = (((R1 @ X31) @ Y31) & ((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ X32) @ Y32)))))).
% 3.45/1.76 thf(fact_175_process__term_Orel__eq, axiom, (! [B:$tType,A:$tType]: ((((((((proces2029722208s_term @ A) @ A) @ B) @ B) @ (^ [Y6:A,Z:A]: ((Y6 = Z)))) @ (^ [Y6:B,Z:B]: ((Y6 = Z)))) = (^ [Y6:((proces554692349s_term @ A) @ B),Z:((proces554692349s_term @ A) @ B)]: ((Y6 = Z))))))).
% 3.45/1.76 thf(fact_176_process__term_Orel__refl, axiom, (! [D:$tType,C:$tType,R1a:(C > (C > $o)),R2a:(D > (D > $o)),X7:((proces554692349s_term @ C) @ D)]: (((! [X6:C]: (((R1a @ X6) @ X6))) => ((! [X6:D]: (((R2a @ X6) @ X6))) => ((((((((proces2029722208s_term @ C) @ C) @ D) @ D) @ R1a) @ R2a) @ X7) @ X7)))))).
% 3.45/1.76 thf(fact_177_process__term_Orel__inject_I2_J, axiom, (! [C:$tType,Pvar:$tType,A:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X2:(proces634752977rocess @ A),Y2:(proces634752977rocess @ B)]: ((((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ (((proces1062592052s_PROC @ A) @ Pvar) @ X2)) @ (((proces1062592052s_PROC @ B) @ C) @ Y2)) = (((((proces749077512rocess @ A) @ B) @ R1) @ X2) @ Y2))))).
% 3.45/1.76 thf(fact_178_process__term_Orel__intros_I2_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),X2:(proces634752977rocess @ A),Y2:(proces634752977rocess @ B),R22:(Pvar > (C > $o))]: (((((((proces749077512rocess @ A) @ B) @ R1) @ X2) @ Y2) => ((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ (((proces1062592052s_PROC @ A) @ Pvar) @ X2)) @ (((proces1062592052s_PROC @ B) @ C) @ Y2)))))).
% 3.45/1.76 thf(fact_179_process__term_Orel__distinct_I1_J, axiom, (! [Pvar:$tType,A:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X1:Pvar,Y2:(proces634752977rocess @ B)]: ((~ (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ (((proces1627516585ss_VAR @ Pvar) @ A) @ X1)) @ (((proces1062592052s_PROC @ B) @ C) @ Y2))))))).
% 3.45/1.76 thf(fact_180_process__term_Orel__distinct_I2_J, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,R1:(A > (C > $o)),R22:(B > (D > $o)),Y2:(proces634752977rocess @ A),X1:D]: ((~ (((((((((proces2029722208s_term @ A) @ C) @ B) @ D) @ R1) @ R22) @ (((proces1062592052s_PROC @ A) @ B) @ Y2)) @ (((proces1627516585ss_VAR @ D) @ C) @ X1))))))).
% 3.45/1.76 thf(fact_181_process__term_Orel__distinct_I9_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X2:(proces634752977rocess @ A),Y41:((proces554692349s_term @ B) @ C),Y42:((proces554692349s_term @ B) @ C)]: ((~ (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ (((proces1062592052s_PROC @ A) @ Pvar) @ X2)) @ ((((proces89589571ess_CH @ B) @ C) @ Y41) @ Y42))))))).
% 3.45/1.76 thf(fact_182_process__term_Orel__distinct_I10_J, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,R1:(A > (C > $o)),R22:(B > (D > $o)),Y41:((proces554692349s_term @ A) @ B),Y42:((proces554692349s_term @ A) @ B),X2:(proces634752977rocess @ C)]: ((~ (((((((((proces2029722208s_term @ A) @ C) @ B) @ D) @ R1) @ R22) @ ((((proces89589571ess_CH @ A) @ B) @ Y41) @ Y42)) @ (((proces1062592052s_PROC @ C) @ D) @ X2))))))).
% 3.45/1.76 thf(fact_183_process__term_Orel__distinct_I7_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X2:(proces634752977rocess @ A),Y31:B,Y32:((proces554692349s_term @ B) @ C)]: ((~ (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ (((proces1062592052s_PROC @ A) @ Pvar) @ X2)) @ ((((proces1454156180ss_ACT @ B) @ C) @ Y31) @ Y32))))))).
% 3.45/1.76 thf(fact_184_process__term_Orel__distinct_I8_J, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,R1:(A > (C > $o)),R22:(B > (D > $o)),Y31:A,Y32:((proces554692349s_term @ A) @ B),X2:(proces634752977rocess @ C)]: ((~ (((((((((proces2029722208s_term @ A) @ C) @ B) @ D) @ R1) @ R22) @ ((((proces1454156180ss_ACT @ A) @ B) @ Y31) @ Y32)) @ (((proces1062592052s_PROC @ C) @ D) @ X2))))))).
% 3.45/1.76 thf(fact_185_process__term_Orel__distinct_I6_J, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,R1:(A > (C > $o)),R22:(B > (D > $o)),Y41:((proces554692349s_term @ A) @ B),Y42:((proces554692349s_term @ A) @ B),X1:D]: ((~ (((((((((proces2029722208s_term @ A) @ C) @ B) @ D) @ R1) @ R22) @ ((((proces89589571ess_CH @ A) @ B) @ Y41) @ Y42)) @ (((proces1627516585ss_VAR @ D) @ C) @ X1))))))).
% 3.45/1.76 thf(fact_186_process__term_Orel__distinct_I5_J, axiom, (! [Pvar:$tType,A:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X1:Pvar,Y41:((proces554692349s_term @ B) @ C),Y42:((proces554692349s_term @ B) @ C)]: ((~ (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ (((proces1627516585ss_VAR @ Pvar) @ A) @ X1)) @ ((((proces89589571ess_CH @ B) @ C) @ Y41) @ Y42))))))).
% 3.45/1.76 thf(fact_187_process__term_Orel__distinct_I4_J, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,R1:(A > (C > $o)),R22:(B > (D > $o)),Y31:A,Y32:((proces554692349s_term @ A) @ B),X1:D]: ((~ (((((((((proces2029722208s_term @ A) @ C) @ B) @ D) @ R1) @ R22) @ ((((proces1454156180ss_ACT @ A) @ B) @ Y31) @ Y32)) @ (((proces1627516585ss_VAR @ D) @ C) @ X1))))))).
% 3.45/1.76 thf(fact_188_process__term_Orel__distinct_I3_J, axiom, (! [Pvar:$tType,A:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X1:Pvar,Y31:B,Y32:((proces554692349s_term @ B) @ C)]: ((~ (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ (((proces1627516585ss_VAR @ Pvar) @ A) @ X1)) @ ((((proces1454156180ss_ACT @ B) @ C) @ Y31) @ Y32))))))).
% 3.45/1.76 thf(fact_189_process__term_Orel__distinct_I12_J, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,R1:(A > (C > $o)),R22:(B > (D > $o)),Y41:((proces554692349s_term @ A) @ B),Y42:((proces554692349s_term @ A) @ B),X31:C,X32:((proces554692349s_term @ C) @ D)]: ((~ (((((((((proces2029722208s_term @ A) @ C) @ B) @ D) @ R1) @ R22) @ ((((proces89589571ess_CH @ A) @ B) @ Y41) @ Y42)) @ ((((proces1454156180ss_ACT @ C) @ D) @ X31) @ X32))))))).
% 3.45/1.76 thf(fact_190_process__term_Orel__distinct_I11_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o)),X31:A,X32:((proces554692349s_term @ A) @ Pvar),Y41:((proces554692349s_term @ B) @ C),Y42:((proces554692349s_term @ B) @ C)]: ((~ (((((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22) @ ((((proces1454156180ss_ACT @ A) @ Pvar) @ X31) @ X32)) @ ((((proces89589571ess_CH @ B) @ C) @ Y41) @ Y42))))))).
% 3.45/1.76 thf(fact_191_accp_Ocases, axiom, (! [A:$tType,R3:(A > (A > $o)),A2:A]: (((((accp @ A) @ R3) @ A2) => (! [Y7:A]: ((((R3 @ Y7) @ A2) => (((accp @ A) @ R3) @ Y7)))))))).
% 3.45/1.76 thf(fact_192_accp_Osimps, axiom, (! [A:$tType]: (((accp @ A) = (^ [R4:(A > (A > $o)),A5:A]: ((? [X:A]: (((A5 = X) & (! [Y5:A]: ((((R4 @ Y5) @ X) => (((accp @ A) @ R4) @ Y5))))))))))))).
% 3.45/1.76 thf(fact_193_accp_Ointros, axiom, (! [A:$tType,R3:(A > (A > $o)),X7:A]: (((! [Y4:A]: ((((R3 @ Y4) @ X7) => (((accp @ A) @ R3) @ Y4)))) => (((accp @ A) @ R3) @ X7))))).
% 3.45/1.76 thf(fact_194_accp__induct__rule, axiom, (! [A:$tType,R3:(A > (A > $o)),A2:A,P3:(A > $o)]: (((((accp @ A) @ R3) @ A2) => ((! [X6:A]: (((((accp @ A) @ R3) @ X6) => ((! [Y7:A]: ((((R3 @ Y7) @ X6) => (P3 @ Y7)))) => (P3 @ X6))))) => (P3 @ A2)))))).
% 3.45/1.76 thf(fact_195_not__accp__down, axiom, (! [A:$tType,R:(A > (A > $o)),X7:A]: (((~ ((((accp @ A) @ R) @ X7))) => (~ ((! [Z3:A]: ((((R @ Z3) @ X7) => (((accp @ A) @ R) @ Z3)))))))))).
% 3.45/1.76 thf(fact_196_accp__downward, axiom, (! [A:$tType,R3:(A > (A > $o)),B2:A,A2:A]: (((((accp @ A) @ R3) @ B2) => (((R3 @ A2) @ B2) => (((accp @ A) @ R3) @ A2)))))).
% 3.45/1.76 thf(fact_197_accp_Oinducts, axiom, (! [A:$tType,R3:(A > (A > $o)),X7:A,P3:(A > $o)]: (((((accp @ A) @ R3) @ X7) => ((! [X6:A]: (((! [Y7:A]: ((((R3 @ Y7) @ X6) => (((accp @ A) @ R3) @ Y7)))) => ((! [Y7:A]: ((((R3 @ Y7) @ X6) => (P3 @ Y7)))) => (P3 @ X6))))) => (P3 @ X7)))))).
% 3.45/1.76 thf(fact_198_accp__induct, axiom, (! [A:$tType,R3:(A > (A > $o)),A2:A,P3:(A > $o)]: (((((accp @ A) @ R3) @ A2) => ((! [X6:A]: (((((accp @ A) @ R3) @ X6) => ((! [Y7:A]: ((((R3 @ Y7) @ X6) => (P3 @ Y7)))) => (P3 @ X6))))) => (P3 @ A2)))))).
% 3.45/1.76 thf(fact_199_in__lex__prod, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A6:A,B3:B,R3:(set @ ((product_prod @ A) @ A)),S2:(set @ ((product_prod @ B) @ B))]: (((((member @ ((product_prod @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B))) @ ((((product_Pair @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ A2) @ B2)) @ ((((product_Pair @ A) @ B) @ A6) @ B3))) @ ((((lex_prod @ A) @ B) @ R3) @ S2)) = ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ A6)) @ R3) | ((A2 = A6) & (((member @ ((product_prod @ B) @ B)) @ ((((product_Pair @ B) @ B) @ B2) @ B3)) @ S2))))))).
% 3.45/1.76 thf(fact_200_process_Ocorec__code, axiom, (! [A:$tType,C:$tType]: ((((proces894737309rocess @ C) @ A) = (^ [P5:(C > $o),G11:(C > A),Q12:(C > $o),G121:(C > (proces634752977rocess @ A)),G122:(C > C),Q21:(C > $o),G211:(C > (proces634752977rocess @ A)),G212:(C > C),Q22:(C > $o),G221:(C > (proces634752977rocess @ A)),G222:(C > C),A5:C]: (((((if @ (proces634752977rocess @ A)) @ (P5 @ A5)) @ (((proces1525233512Action @ A) @ (G11 @ A5)) @ ((((if @ (proces634752977rocess @ A)) @ (Q12 @ A5)) @ (G121 @ A5)) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P5) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ (G122 @ A5))))) @ (((proces1915862579Choice @ A) @ ((((if @ (proces634752977rocess @ A)) @ (Q21 @ A5)) @ (G211 @ A5)) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P5) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ (G212 @ A5)))) @ ((((if @ (proces634752977rocess @ A)) @ (Q22 @ A5)) @ (G221 @ A5)) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P5) @ G11) @ Q12) @ G121) @ G122) @ Q21) @ G211) @ G212) @ Q22) @ G221) @ G222) @ (G222 @ A5))))))))))).
% 3.45/1.76 thf(fact_201_process_Ocorec__disc__iff_I1_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),G112:(C > A),Q122:(C > $o),G1212:(C > (proces634752977rocess @ A)),G1222:(C > C),Q212:(C > $o),G2112:(C > (proces634752977rocess @ A)),G2122:(C > C),Q222:(C > $o),G2212:(C > (proces634752977rocess @ A)),G2222:(C > C),A2:C]: ((((proces10484146Action @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ A2)) = (P @ A2))))).
% 3.45/1.76 thf(fact_202_process_Ocorec__disc__iff_I2_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),G112:(C > A),Q122:(C > $o),G1212:(C > (proces634752977rocess @ A)),G1222:(C > C),Q212:(C > $o),G2112:(C > (proces634752977rocess @ A)),G2122:(C > C),Q222:(C > $o),G2212:(C > (proces634752977rocess @ A)),G2222:(C > C),A2:C]: ((((proces401113213Choice @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ A2)) = (~ ((P @ A2))))))).
% 3.45/1.76 thf(fact_203_process_Ocorec__disc_I1_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),A2:C,G112:(C > A),Q122:(C > $o),G1212:(C > (proces634752977rocess @ A)),G1222:(C > C),Q212:(C > $o),G2112:(C > (proces634752977rocess @ A)),G2122:(C > C),Q222:(C > $o),G2212:(C > (proces634752977rocess @ A)),G2222:(C > C)]: (((P @ A2) => ((proces10484146Action @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ A2)))))).
% 3.45/1.76 thf(fact_204_process_Ocorec_I1_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),A2:C,G112:(C > A),Q122:(C > $o),G1212:(C > (proces634752977rocess @ A)),G1222:(C > C),Q212:(C > $o),G2112:(C > (proces634752977rocess @ A)),G2122:(C > C),Q222:(C > $o),G2212:(C > (proces634752977rocess @ A)),G2222:(C > C)]: (((P @ A2) => (((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ A2) = (((proces1525233512Action @ A) @ (G112 @ A2)) @ ((((if @ (proces634752977rocess @ A)) @ (Q122 @ A2)) @ (G1212 @ A2)) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ (G1222 @ A2))))))))).
% 3.45/1.76 thf(fact_205_process_Ocorec_I2_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),A2:C,G112:(C > A),Q122:(C > $o),G1212:(C > (proces634752977rocess @ A)),G1222:(C > C),Q212:(C > $o),G2112:(C > (proces634752977rocess @ A)),G2122:(C > C),Q222:(C > $o),G2212:(C > (proces634752977rocess @ A)),G2222:(C > C)]: (((~ ((P @ A2))) => (((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ A2) = (((proces1915862579Choice @ A) @ ((((if @ (proces634752977rocess @ A)) @ (Q212 @ A2)) @ (G2112 @ A2)) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ (G2122 @ A2)))) @ ((((if @ (proces634752977rocess @ A)) @ (Q222 @ A2)) @ (G2212 @ A2)) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ (G2222 @ A2))))))))).
% 3.45/1.76 thf(fact_206_process_Ocorec__disc_I2_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),A2:C,G112:(C > A),Q122:(C > $o),G1212:(C > (proces634752977rocess @ A)),G1222:(C > C),Q212:(C > $o),G2112:(C > (proces634752977rocess @ A)),G2122:(C > C),Q222:(C > $o),G2212:(C > (proces634752977rocess @ A)),G2222:(C > C)]: (((~ ((P @ A2))) => ((proces401113213Choice @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ A2)))))).
% 3.45/1.76 thf(fact_207_process_Ocorec__sel_I2_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),A2:C,Q122:(C > $o),G112:(C > A),G1212:(C > (proces634752977rocess @ A)),G1222:(C > C),Q212:(C > $o),G2112:(C > (proces634752977rocess @ A)),G2122:(C > C),Q222:(C > $o),G2212:(C > (proces634752977rocess @ A)),G2222:(C > C)]: (((P @ A2) => (((Q122 @ A2) => (((proces1778668539contOf @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ A2)) = (G1212 @ A2))) & ((~ ((Q122 @ A2))) => (((proces1778668539contOf @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ A2)) = ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ (G1222 @ A2))))))))).
% 3.45/1.76 thf(fact_208_process_Ocorec__sel_I3_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),A2:C,Q212:(C > $o),G112:(C > A),Q122:(C > $o),G1212:(C > (proces634752977rocess @ A)),G1222:(C > C),G2112:(C > (proces634752977rocess @ A)),G2122:(C > C),Q222:(C > $o),G2212:(C > (proces634752977rocess @ A)),G2222:(C > C)]: (((~ ((P @ A2))) => (((Q212 @ A2) => (((proces979765041_ch1Of @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ A2)) = (G2112 @ A2))) & ((~ ((Q212 @ A2))) => (((proces979765041_ch1Of @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ A2)) = ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ (G2122 @ A2))))))))).
% 3.45/1.76 thf(fact_209_process_Ocorec__sel_I4_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),A2:C,Q222:(C > $o),G112:(C > A),Q122:(C > $o),G1212:(C > (proces634752977rocess @ A)),G1222:(C > C),Q212:(C > $o),G2112:(C > (proces634752977rocess @ A)),G2122:(C > C),G2212:(C > (proces634752977rocess @ A)),G2222:(C > C)]: (((~ ((P @ A2))) => (((Q222 @ A2) => (((proces988026546_ch2Of @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ A2)) = (G2212 @ A2))) & ((~ ((Q222 @ A2))) => (((proces988026546_ch2Of @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ A2)) = ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ (G2222 @ A2))))))))).
% 3.45/1.76 thf(fact_210_process_Ocorec__sel_I1_J, axiom, (! [A:$tType,C:$tType,P:(C > $o),A2:C,G112:(C > A),Q122:(C > $o),G1212:(C > (proces634752977rocess @ A)),G1222:(C > C),Q212:(C > $o),G2112:(C > (proces634752977rocess @ A)),G2122:(C > C),Q222:(C > $o),G2212:(C > (proces634752977rocess @ A)),G2222:(C > C)]: (((P @ A2) => (((proces745025900prefOf @ A) @ ((((((((((((((proces894737309rocess @ C) @ A) @ P) @ G112) @ Q122) @ G1212) @ G1222) @ Q212) @ G2112) @ G2122) @ Q222) @ G2212) @ G2222) @ A2)) = (G112 @ A2)))))).
% 3.45/1.76 thf(fact_211_same__fstI, axiom, (! [B:$tType,A:$tType,P3:(A > $o),X7:A,Y8:B,Y3:B,R:(A > (set @ ((product_prod @ B) @ B)))]: (((P3 @ X7) => ((((member @ ((product_prod @ B) @ B)) @ ((((product_Pair @ B) @ B) @ Y8) @ Y3)) @ (R @ X7)) => (((member @ ((product_prod @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B))) @ ((((product_Pair @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X7) @ Y8)) @ ((((product_Pair @ A) @ B) @ X7) @ Y3))) @ ((((same_fst @ A) @ B) @ P3) @ R))))))).
% 3.45/1.76 thf(fact_212_ssubst__Pair__rhs, axiom, (! [B:$tType,A:$tType,R3:A,S2:B,R:(set @ ((product_prod @ A) @ B)),S3:B]: (((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ R3) @ S2)) @ R) => ((S3 = S2) => (((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ R3) @ S3)) @ R)))))).
% 3.45/1.76 thf(fact_213_cut__def, axiom, (! [B:$tType,A:$tType]: ((((cut @ A) @ B) = (^ [F7:(A > B),R2:(set @ ((product_prod @ A) @ A)),X:A,Y5:A]: (((((if @ B) @ (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y5) @ X)) @ R2)) @ (F7 @ Y5)) @ (undefined @ B)))))))).
% 3.45/1.76 thf(fact_214_curry__conv, axiom, (! [A:$tType,C:$tType,B:$tType]: (((((product_curry @ B) @ C) @ A) = (^ [F7:(((product_prod @ B) @ C) > A),A5:B,B5:C]: ((F7 @ ((((product_Pair @ B) @ C) @ A5) @ B5)))))))).
% 3.45/1.76 thf(fact_215_curryI, axiom, (! [A:$tType,B:$tType,F:(((product_prod @ A) @ B) > $o),A2:A,B2:B]: (((F @ ((((product_Pair @ A) @ B) @ A2) @ B2)) => ((((((product_curry @ A) @ B) @ $o) @ F) @ A2) @ B2))))).
% 3.45/1.76 thf(fact_216_cuts__eq, axiom, (! [B:$tType,A:$tType,F:(A > B),R:(set @ ((product_prod @ A) @ A)),X7:A,G:(A > B)]: ((((((((cut @ A) @ B) @ F) @ R) @ X7) = (((((cut @ A) @ B) @ G) @ R) @ X7)) = (! [Y5:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y5) @ X7)) @ R) => ((F @ Y5) = (G @ Y5))))))))).
% 3.45/1.76 thf(fact_217_cut__apply, axiom, (! [B:$tType,A:$tType,X7:A,A2:A,R:(set @ ((product_prod @ A) @ A)),F:(A > B)]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X7) @ A2)) @ R) => (((((((cut @ A) @ B) @ F) @ R) @ A2) @ X7) = (F @ X7)))))).
% 3.45/1.76 thf(fact_218_curry__K, axiom, (! [B:$tType,C:$tType,A:$tType,C3:C]: ((((((product_curry @ A) @ B) @ C) @ (^ [X:((product_prod @ A) @ B)]: (C3))) = (^ [X:A,Y5:B]: (C3)))))).
% 3.45/1.76 thf(fact_219_curryD, axiom, (! [A:$tType,B:$tType,F:(((product_prod @ A) @ B) > $o),A2:A,B2:B]: ((((((((product_curry @ A) @ B) @ $o) @ F) @ A2) @ B2) => (F @ ((((product_Pair @ A) @ B) @ A2) @ B2)))))).
% 3.45/1.76 thf(fact_220_curryE, axiom, (! [A:$tType,B:$tType,F:(((product_prod @ A) @ B) > $o),A2:A,B2:B]: ((((((((product_curry @ A) @ B) @ $o) @ F) @ A2) @ B2) => (F @ ((((product_Pair @ A) @ B) @ A2) @ B2)))))).
% 3.45/1.76 thf(fact_221_curry__def, axiom, (! [C:$tType,B:$tType,A:$tType]: (((((product_curry @ A) @ B) @ C) = (^ [C4:(((product_prod @ A) @ B) > C),X:A,Y5:B]: ((C4 @ ((((product_Pair @ A) @ B) @ X) @ Y5)))))))).
% 3.45/1.76 thf(fact_222_adm__lemma, axiom, (! [B:$tType,A:$tType,R:(set @ ((product_prod @ A) @ A)),F8:((A > B) > (A > B))]: (((((adm_wf @ A) @ B) @ R) @ (^ [F7:(A > B),X:A]: (((F8 @ (((((cut @ A) @ B) @ F7) @ R) @ X)) @ X))))))).
% 3.45/1.76 thf(fact_223_accp__acc__eq, axiom, (! [A:$tType,R3:(set @ ((product_prod @ A) @ A))]: ((((accp @ A) @ (^ [X:A,Y5:A]: ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Y5)) @ R3)))) = (^ [X:A]: ((((member @ A) @ X) @ ((acc @ A) @ R3)))))))).
% 3.45/1.76 thf(fact_224_acc_Ocases, axiom, (! [A:$tType,A2:A,R3:(set @ ((product_prod @ A) @ A))]: (((((member @ A) @ A2) @ ((acc @ A) @ R3)) => (! [Y7:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y7) @ A2)) @ R3) => (((member @ A) @ Y7) @ ((acc @ A) @ R3))))))))).
% 3.45/1.76 thf(fact_225_acc_Osimps, axiom, (! [A:$tType,A2:A,R3:(set @ ((product_prod @ A) @ A))]: (((((member @ A) @ A2) @ ((acc @ A) @ R3)) = (? [X:A]: (((A2 = X) & (! [Y5:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y5) @ X)) @ R3) => (((member @ A) @ Y5) @ ((acc @ A) @ R3)))))))))))).
% 3.45/1.76 thf(fact_226_acc_Ointros, axiom, (! [A:$tType,X7:A,R3:(set @ ((product_prod @ A) @ A))]: (((! [Y4:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y4) @ X7)) @ R3) => (((member @ A) @ Y4) @ ((acc @ A) @ R3))))) => (((member @ A) @ X7) @ ((acc @ A) @ R3)))))).
% 3.45/1.76 thf(fact_227_acc__induct, axiom, (! [A:$tType,A2:A,R3:(set @ ((product_prod @ A) @ A)),P3:(A > $o)]: (((((member @ A) @ A2) @ ((acc @ A) @ R3)) => ((! [X6:A]: (((((member @ A) @ X6) @ ((acc @ A) @ R3)) => ((! [Y7:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y7) @ X6)) @ R3) => (P3 @ Y7)))) => (P3 @ X6))))) => (P3 @ A2)))))).
% 3.45/1.76 thf(fact_228_acc_Oinducts, axiom, (! [A:$tType,X7:A,R3:(set @ ((product_prod @ A) @ A)),P3:(A > $o)]: (((((member @ A) @ X7) @ ((acc @ A) @ R3)) => ((! [X6:A]: (((! [Y7:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y7) @ X6)) @ R3) => (((member @ A) @ Y7) @ ((acc @ A) @ R3))))) => ((! [Y7:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y7) @ X6)) @ R3) => (P3 @ Y7)))) => (P3 @ X6))))) => (P3 @ X7)))))).
% 3.45/1.76 thf(fact_229_acc__downward, axiom, (! [A:$tType,B2:A,R3:(set @ ((product_prod @ A) @ A)),A2:A]: (((((member @ A) @ B2) @ ((acc @ A) @ R3)) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ R3) => (((member @ A) @ A2) @ ((acc @ A) @ R3))))))).
% 3.45/1.76 thf(fact_230_not__acc__down, axiom, (! [A:$tType,X7:A,R:(set @ ((product_prod @ A) @ A))]: (((~ ((((member @ A) @ X7) @ ((acc @ A) @ R)))) => (~ ((! [Z3:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Z3) @ X7)) @ R) => (((member @ A) @ Z3) @ ((acc @ A) @ R))))))))))).
% 3.45/1.76 thf(fact_231_acc__induct__rule, axiom, (! [A:$tType,A2:A,R3:(set @ ((product_prod @ A) @ A)),P3:(A > $o)]: (((((member @ A) @ A2) @ ((acc @ A) @ R3)) => ((! [X6:A]: (((((member @ A) @ X6) @ ((acc @ A) @ R3)) => ((! [Y7:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Y7) @ X6)) @ R3) => (P3 @ Y7)))) => (P3 @ X6))))) => (P3 @ A2)))))).
% 3.45/1.76 thf(fact_232_adm__wf__def, axiom, (! [B:$tType,A:$tType]: ((((adm_wf @ A) @ B) = (^ [R2:(set @ ((product_prod @ A) @ A)),F9:((A > B) > (A > B))]: ((! [F7:(A > B),G4:(A > B),X:A]: (((! [Z4:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ Z4) @ X)) @ R2) => ((F7 @ Z4) = (G4 @ Z4))))) => (((F9 @ F7) @ X) = ((F9 @ G4) @ X))))))))))).
% 3.45/1.76 thf(fact_233_acc__def, axiom, (! [A:$tType]: (((acc @ A) = (^ [R4:(set @ ((product_prod @ A) @ A))]: (((collect @ A) @ ((accp @ A) @ (^ [X:A,Y5:A]: ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Y5)) @ R4))))))))))).
% 3.45/1.76 thf(fact_234_process__term_Octr__transfer_I2_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o))]: (((((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ (((proces749077512rocess @ A) @ B) @ R1)) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22)) @ ((proces1062592052s_PROC @ A) @ Pvar)) @ ((proces1062592052s_PROC @ B) @ C))))).
% 3.45/1.76 thf(fact_235_in__inv__image, axiom, (! [A:$tType,B:$tType,X7:A,Y3:A,R3:(set @ ((product_prod @ B) @ B)),F:(A > B)]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X7) @ Y3)) @ ((((inv_image @ B) @ A) @ R3) @ F)) = (((member @ ((product_prod @ B) @ B)) @ ((((product_Pair @ B) @ B) @ (F @ X7)) @ (F @ Y3))) @ R3))))).
% 3.45/1.76 thf(fact_236_process__term_Octr__transfer_I1_J, axiom, (! [Pvar:$tType,A:$tType,B:$tType,C:$tType,R22:(Pvar > (C > $o)),R1:(A > (B > $o))]: (((((((((bNF_rel_fun @ Pvar) @ C) @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ R22) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22)) @ ((proces1627516585ss_VAR @ Pvar) @ A)) @ ((proces1627516585ss_VAR @ C) @ B))))).
% 3.45/1.76 thf(fact_237_process__term_Orec__transfer, axiom, (! [Pvar:$tType,D:$tType,A:$tType,B:$tType,E:$tType,C:$tType,R22:(Pvar > (C > $o)),S:(D > (E > $o)),R1:(A > (B > $o))]: (((((((((bNF_rel_fun @ (Pvar > D)) @ (C > E)) @ (((proces634752977rocess @ A) > D) > ((A > (((proces554692349s_term @ A) @ Pvar) > (D > D))) > ((((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > (D > (D > D)))) > (((proces554692349s_term @ A) @ Pvar) > D))))) @ (((proces634752977rocess @ B) > E) > ((B > (((proces554692349s_term @ B) @ C) > (E > E))) > ((((proces554692349s_term @ B) @ C) > (((proces554692349s_term @ B) @ C) > (E > (E > E)))) > (((proces554692349s_term @ B) @ C) > E))))) @ ((((((bNF_rel_fun @ Pvar) @ C) @ D) @ E) @ R22) @ S)) @ ((((((bNF_rel_fun @ ((proces634752977rocess @ A) > D)) @ ((proces634752977rocess @ B) > E)) @ ((A > (((proces554692349s_term @ A) @ Pvar) > (D > D))) > ((((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > (D > (D > D)))) > (((proces554692349s_term @ A) @ Pvar) > D)))) @ ((B > (((proces554692349s_term @ B) @ C) > (E > E))) > ((((proces554692349s_term @ B) @ C) > (((proces554692349s_term @ B) @ C) > (E > (E > E)))) > (((proces554692349s_term @ B) @ C) > E)))) @ ((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ D) @ E) @ (((proces749077512rocess @ A) @ B) @ R1)) @ S)) @ ((((((bNF_rel_fun @ (A > (((proces554692349s_term @ A) @ Pvar) > (D > D)))) @ (B > (((proces554692349s_term @ B) @ C) > (E > E)))) @ ((((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > (D > (D > D)))) > (((proces554692349s_term @ A) @ Pvar) > D))) @ ((((proces554692349s_term @ B) @ C) > (((proces554692349s_term @ B) @ C) > (E > (E > E)))) > (((proces554692349s_term @ B) @ C) > E))) @ ((((((bNF_rel_fun @ A) @ B) @ (((proces554692349s_term @ A) @ Pvar) > (D > D))) @ (((proces554692349s_term @ B) @ C) > (E > E))) @ R1) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ (D > D)) @ (E > E)) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22)) @ ((((((bNF_rel_fun @ D) @ E) @ D) @ E) @ S) @ S)))) @ ((((((bNF_rel_fun @ (((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > (D > (D > D))))) @ (((proces554692349s_term @ B) @ C) > (((proces554692349s_term @ B) @ C) > (E > (E > E))))) @ (((proces554692349s_term @ A) @ Pvar) > D)) @ (((proces554692349s_term @ B) @ C) > E)) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ (((proces554692349s_term @ A) @ Pvar) > (D > (D > D)))) @ (((proces554692349s_term @ B) @ C) > (E > (E > E)))) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22)) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ (D > (D > D))) @ (E > (E > E))) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22)) @ ((((((bNF_rel_fun @ D) @ E) @ (D > D)) @ (E > E)) @ S) @ ((((((bNF_rel_fun @ D) @ E) @ D) @ E) @ S) @ S))))) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ D) @ E) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22)) @ S))))) @ (((proces2117273769s_term @ Pvar) @ D) @ A)) @ (((proces2117273769s_term @ C) @ E) @ B))))).
% 3.45/1.76 thf(fact_238_process__term_Ocase__transfer, axiom, (! [Pvar:$tType,D:$tType,A:$tType,B:$tType,E:$tType,C:$tType,R22:(Pvar > (C > $o)),S:(D > (E > $o)),R1:(A > (B > $o))]: (((((((((bNF_rel_fun @ (Pvar > D)) @ (C > E)) @ (((proces634752977rocess @ A) > D) > ((A > (((proces554692349s_term @ A) @ Pvar) > D)) > ((((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > D)) > (((proces554692349s_term @ A) @ Pvar) > D))))) @ (((proces634752977rocess @ B) > E) > ((B > (((proces554692349s_term @ B) @ C) > E)) > ((((proces554692349s_term @ B) @ C) > (((proces554692349s_term @ B) @ C) > E)) > (((proces554692349s_term @ B) @ C) > E))))) @ ((((((bNF_rel_fun @ Pvar) @ C) @ D) @ E) @ R22) @ S)) @ ((((((bNF_rel_fun @ ((proces634752977rocess @ A) > D)) @ ((proces634752977rocess @ B) > E)) @ ((A > (((proces554692349s_term @ A) @ Pvar) > D)) > ((((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > D)) > (((proces554692349s_term @ A) @ Pvar) > D)))) @ ((B > (((proces554692349s_term @ B) @ C) > E)) > ((((proces554692349s_term @ B) @ C) > (((proces554692349s_term @ B) @ C) > E)) > (((proces554692349s_term @ B) @ C) > E)))) @ ((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ D) @ E) @ (((proces749077512rocess @ A) @ B) @ R1)) @ S)) @ ((((((bNF_rel_fun @ (A > (((proces554692349s_term @ A) @ Pvar) > D))) @ (B > (((proces554692349s_term @ B) @ C) > E))) @ ((((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > D)) > (((proces554692349s_term @ A) @ Pvar) > D))) @ ((((proces554692349s_term @ B) @ C) > (((proces554692349s_term @ B) @ C) > E)) > (((proces554692349s_term @ B) @ C) > E))) @ ((((((bNF_rel_fun @ A) @ B) @ (((proces554692349s_term @ A) @ Pvar) > D)) @ (((proces554692349s_term @ B) @ C) > E)) @ R1) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ D) @ E) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22)) @ S))) @ ((((((bNF_rel_fun @ (((proces554692349s_term @ A) @ Pvar) > (((proces554692349s_term @ A) @ Pvar) > D))) @ (((proces554692349s_term @ B) @ C) > (((proces554692349s_term @ B) @ C) > E))) @ (((proces554692349s_term @ A) @ Pvar) > D)) @ (((proces554692349s_term @ B) @ C) > E)) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ (((proces554692349s_term @ A) @ Pvar) > D)) @ (((proces554692349s_term @ B) @ C) > E)) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22)) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ D) @ E) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22)) @ S))) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ D) @ E) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22)) @ S))))) @ (((proces460752237s_term @ Pvar) @ D) @ A)) @ (((proces460752237s_term @ C) @ E) @ B))))).
% 3.45/1.76 thf(fact_239_process_Ocorec__transfer, axiom, (! [C:$tType,A:$tType,B:$tType,D:$tType,S:(C > (D > $o)),R:(A > (B > $o))]: (((((((((bNF_rel_fun @ (C > $o)) @ (D > $o)) @ ((C > A) > ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > (C > (proces634752977rocess @ A))))))))))))) @ ((D > B) > ((D > $o) > ((D > (proces634752977rocess @ B)) > ((D > D) > ((D > $o) > ((D > (proces634752977rocess @ B)) > ((D > D) > ((D > $o) > ((D > (proces634752977rocess @ B)) > ((D > D) > (D > (proces634752977rocess @ B))))))))))))) @ ((((((bNF_rel_fun @ C) @ D) @ $o) @ $o) @ S) @ (^ [Y6:$o,Z:$o]: ((Y6 = Z))))) @ ((((((bNF_rel_fun @ (C > A)) @ (D > B)) @ ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > (C > (proces634752977rocess @ A)))))))))))) @ ((D > $o) > ((D > (proces634752977rocess @ B)) > ((D > D) > ((D > $o) > ((D > (proces634752977rocess @ B)) > ((D > D) > ((D > $o) > ((D > (proces634752977rocess @ B)) > ((D > D) > (D > (proces634752977rocess @ B)))))))))))) @ ((((((bNF_rel_fun @ C) @ D) @ A) @ B) @ S) @ R)) @ ((((((bNF_rel_fun @ (C > $o)) @ (D > $o)) @ ((C > (proces634752977rocess @ A)) > ((C > C) > ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > (C > (proces634752977rocess @ A))))))))))) @ ((D > (proces634752977rocess @ B)) > ((D > D) > ((D > $o) > ((D > (proces634752977rocess @ B)) > ((D > D) > ((D > $o) > ((D > (proces634752977rocess @ B)) > ((D > D) > (D > (proces634752977rocess @ B))))))))))) @ ((((((bNF_rel_fun @ C) @ D) @ $o) @ $o) @ S) @ (^ [Y6:$o,Z:$o]: ((Y6 = Z))))) @ ((((((bNF_rel_fun @ (C > (proces634752977rocess @ A))) @ (D > (proces634752977rocess @ B))) @ ((C > C) > ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > (C > (proces634752977rocess @ A)))))))))) @ ((D > D) > ((D > $o) > ((D > (proces634752977rocess @ B)) > ((D > D) > ((D > $o) > ((D > (proces634752977rocess @ B)) > ((D > D) > (D > (proces634752977rocess @ B)))))))))) @ ((((((bNF_rel_fun @ C) @ D) @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ S) @ (((proces749077512rocess @ A) @ B) @ R))) @ ((((((bNF_rel_fun @ (C > C)) @ (D > D)) @ ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > (C > (proces634752977rocess @ A))))))))) @ ((D > $o) > ((D > (proces634752977rocess @ B)) > ((D > D) > ((D > $o) > ((D > (proces634752977rocess @ B)) > ((D > D) > (D > (proces634752977rocess @ B))))))))) @ ((((((bNF_rel_fun @ C) @ D) @ C) @ D) @ S) @ S)) @ ((((((bNF_rel_fun @ (C > $o)) @ (D > $o)) @ ((C > (proces634752977rocess @ A)) > ((C > C) > ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > (C > (proces634752977rocess @ A)))))))) @ ((D > (proces634752977rocess @ B)) > ((D > D) > ((D > $o) > ((D > (proces634752977rocess @ B)) > ((D > D) > (D > (proces634752977rocess @ B)))))))) @ ((((((bNF_rel_fun @ C) @ D) @ $o) @ $o) @ S) @ (^ [Y6:$o,Z:$o]: ((Y6 = Z))))) @ ((((((bNF_rel_fun @ (C > (proces634752977rocess @ A))) @ (D > (proces634752977rocess @ B))) @ ((C > C) > ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > (C > (proces634752977rocess @ A))))))) @ ((D > D) > ((D > $o) > ((D > (proces634752977rocess @ B)) > ((D > D) > (D > (proces634752977rocess @ B))))))) @ ((((((bNF_rel_fun @ C) @ D) @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ S) @ (((proces749077512rocess @ A) @ B) @ R))) @ ((((((bNF_rel_fun @ (C > C)) @ (D > D)) @ ((C > $o) > ((C > (proces634752977rocess @ A)) > ((C > C) > (C > (proces634752977rocess @ A)))))) @ ((D > $o) > ((D > (proces634752977rocess @ B)) > ((D > D) > (D > (proces634752977rocess @ B)))))) @ ((((((bNF_rel_fun @ C) @ D) @ C) @ D) @ S) @ S)) @ ((((((bNF_rel_fun @ (C > $o)) @ (D > $o)) @ ((C > (proces634752977rocess @ A)) > ((C > C) > (C > (proces634752977rocess @ A))))) @ ((D > (proces634752977rocess @ B)) > ((D > D) > (D > (proces634752977rocess @ B))))) @ ((((((bNF_rel_fun @ C) @ D) @ $o) @ $o) @ S) @ (^ [Y6:$o,Z:$o]: ((Y6 = Z))))) @ ((((((bNF_rel_fun @ (C > (proces634752977rocess @ A))) @ (D > (proces634752977rocess @ B))) @ ((C > C) > (C > (proces634752977rocess @ A)))) @ ((D > D) > (D > (proces634752977rocess @ B)))) @ ((((((bNF_rel_fun @ C) @ D) @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ S) @ (((proces749077512rocess @ A) @ B) @ R))) @ ((((((bNF_rel_fun @ (C > C)) @ (D > D)) @ (C > (proces634752977rocess @ A))) @ (D > (proces634752977rocess @ B))) @ ((((((bNF_rel_fun @ C) @ D) @ C) @ D) @ S) @ S)) @ ((((((bNF_rel_fun @ C) @ D) @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ S) @ (((proces749077512rocess @ A) @ B) @ R))))))))))))) @ ((proces894737309rocess @ C) @ A)) @ ((proces894737309rocess @ D) @ B))))).
% 3.45/1.76 thf(fact_240_process_Odisc__transfer_I1_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o))]: (((((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ $o) @ $o) @ (((proces749077512rocess @ A) @ B) @ R)) @ (^ [Y6:$o,Z:$o]: ((Y6 = Z)))) @ (proces10484146Action @ A)) @ (proces10484146Action @ B))))).
% 3.45/1.76 thf(fact_241_process_Odisc__transfer_I2_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o))]: (((((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ $o) @ $o) @ (((proces749077512rocess @ A) @ B) @ R)) @ (^ [Y6:$o,Z:$o]: ((Y6 = Z)))) @ (proces401113213Choice @ A)) @ (proces401113213Choice @ B))))).
% 3.45/1.76 thf(fact_242_process_Octr__transfer_I2_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o))]: (((((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ ((proces634752977rocess @ A) > (proces634752977rocess @ A))) @ ((proces634752977rocess @ B) > (proces634752977rocess @ B))) @ (((proces749077512rocess @ A) @ B) @ R)) @ ((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ (((proces749077512rocess @ A) @ B) @ R)) @ (((proces749077512rocess @ A) @ B) @ R))) @ (proces1915862579Choice @ A)) @ (proces1915862579Choice @ B))))).
% 3.45/1.76 thf(fact_243_process_Ocase__transfer, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,R:(A > (B > $o)),S:(C > (D > $o))]: (((((((((bNF_rel_fun @ (A > ((proces634752977rocess @ A) > C))) @ (B > ((proces634752977rocess @ B) > D))) @ (((proces634752977rocess @ A) > ((proces634752977rocess @ A) > C)) > ((proces634752977rocess @ A) > C))) @ (((proces634752977rocess @ B) > ((proces634752977rocess @ B) > D)) > ((proces634752977rocess @ B) > D))) @ ((((((bNF_rel_fun @ A) @ B) @ ((proces634752977rocess @ A) > C)) @ ((proces634752977rocess @ B) > D)) @ R) @ ((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ C) @ D) @ (((proces749077512rocess @ A) @ B) @ R)) @ S))) @ ((((((bNF_rel_fun @ ((proces634752977rocess @ A) > ((proces634752977rocess @ A) > C))) @ ((proces634752977rocess @ B) > ((proces634752977rocess @ B) > D))) @ ((proces634752977rocess @ A) > C)) @ ((proces634752977rocess @ B) > D)) @ ((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ ((proces634752977rocess @ A) > C)) @ ((proces634752977rocess @ B) > D)) @ (((proces749077512rocess @ A) @ B) @ R)) @ ((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ C) @ D) @ (((proces749077512rocess @ A) @ B) @ R)) @ S))) @ ((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ C) @ D) @ (((proces749077512rocess @ A) @ B) @ R)) @ S))) @ ((proces1406508781rocess @ A) @ C)) @ ((proces1406508781rocess @ B) @ D))))).
% 3.45/1.76 thf(fact_244_process_Opred__transfer, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o))]: (((((((((bNF_rel_fun @ (A > $o)) @ (B > $o)) @ ((proces634752977rocess @ A) > $o)) @ ((proces634752977rocess @ B) > $o)) @ ((((((bNF_rel_fun @ A) @ B) @ $o) @ $o) @ R) @ (^ [Y6:$o,Z:$o]: ((Y6 = Z))))) @ ((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ $o) @ $o) @ (((proces749077512rocess @ A) @ B) @ R)) @ (^ [Y6:$o,Z:$o]: ((Y6 = Z))))) @ (proces1205983068rocess @ A)) @ (proces1205983068rocess @ B))))).
% 3.45/1.76 thf(fact_245_process_Orel__transfer, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,Sa:(A > (C > $o)),Sc:(B > (D > $o))]: (((((((((bNF_rel_fun @ (A > (B > $o))) @ (C > (D > $o))) @ ((proces634752977rocess @ A) > ((proces634752977rocess @ B) > $o))) @ ((proces634752977rocess @ C) > ((proces634752977rocess @ D) > $o))) @ ((((((bNF_rel_fun @ A) @ C) @ (B > $o)) @ (D > $o)) @ Sa) @ ((((((bNF_rel_fun @ B) @ D) @ $o) @ $o) @ Sc) @ (^ [Y6:$o,Z:$o]: ((Y6 = Z)))))) @ ((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ C)) @ ((proces634752977rocess @ B) > $o)) @ ((proces634752977rocess @ D) > $o)) @ (((proces749077512rocess @ A) @ C) @ Sa)) @ ((((((bNF_rel_fun @ (proces634752977rocess @ B)) @ (proces634752977rocess @ D)) @ $o) @ $o) @ (((proces749077512rocess @ B) @ D) @ Sc)) @ (^ [Y6:$o,Z:$o]: ((Y6 = Z)))))) @ ((proces749077512rocess @ A) @ B)) @ ((proces749077512rocess @ C) @ D))))).
% 3.45/1.76 thf(fact_246_process_Octr__transfer_I1_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o))]: (((((((((bNF_rel_fun @ A) @ B) @ ((proces634752977rocess @ A) > (proces634752977rocess @ A))) @ ((proces634752977rocess @ B) > (proces634752977rocess @ B))) @ R) @ ((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ (proces634752977rocess @ A)) @ (proces634752977rocess @ B)) @ (((proces749077512rocess @ A) @ B) @ R)) @ (((proces749077512rocess @ A) @ B) @ R))) @ (proces1525233512Action @ A)) @ (proces1525233512Action @ B))))).
% 3.45/1.76 thf(fact_247_process__term_Octr__transfer_I4_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o))]: (((((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ (((proces554692349s_term @ A) @ Pvar) > ((proces554692349s_term @ A) @ Pvar))) @ (((proces554692349s_term @ B) @ C) > ((proces554692349s_term @ B) @ C))) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22)) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22)) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22))) @ ((proces89589571ess_CH @ A) @ Pvar)) @ ((proces89589571ess_CH @ B) @ C))))).
% 3.45/1.76 thf(fact_248_process__term_Octr__transfer_I3_J, axiom, (! [A:$tType,Pvar:$tType,C:$tType,B:$tType,R1:(A > (B > $o)),R22:(Pvar > (C > $o))]: (((((((((bNF_rel_fun @ A) @ B) @ (((proces554692349s_term @ A) @ Pvar) > ((proces554692349s_term @ A) @ Pvar))) @ (((proces554692349s_term @ B) @ C) > ((proces554692349s_term @ B) @ C))) @ R1) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ ((proces554692349s_term @ A) @ Pvar)) @ ((proces554692349s_term @ B) @ C)) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22)) @ ((((((proces2029722208s_term @ A) @ B) @ Pvar) @ C) @ R1) @ R22))) @ ((proces1454156180ss_ACT @ A) @ Pvar)) @ ((proces1454156180ss_ACT @ B) @ C))))).
% 3.45/1.76 thf(fact_249_process__term_Opred__transfer, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,R1:(A > (C > $o)),R22:(B > (D > $o))]: (((((((((bNF_rel_fun @ (A > $o)) @ (C > $o)) @ ((B > $o) > (((proces554692349s_term @ A) @ B) > $o))) @ ((D > $o) > (((proces554692349s_term @ C) @ D) > $o))) @ ((((((bNF_rel_fun @ A) @ C) @ $o) @ $o) @ R1) @ (^ [Y6:$o,Z:$o]: ((Y6 = Z))))) @ ((((((bNF_rel_fun @ (B > $o)) @ (D > $o)) @ (((proces554692349s_term @ A) @ B) > $o)) @ (((proces554692349s_term @ C) @ D) > $o)) @ ((((((bNF_rel_fun @ B) @ D) @ $o) @ $o) @ R22) @ (^ [Y6:$o,Z:$o]: ((Y6 = Z))))) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ B)) @ ((proces554692349s_term @ C) @ D)) @ $o) @ $o) @ ((((((proces2029722208s_term @ A) @ C) @ B) @ D) @ R1) @ R22)) @ (^ [Y6:$o,Z:$o]: ((Y6 = Z)))))) @ ((proces2118920028s_term @ A) @ B)) @ ((proces2118920028s_term @ C) @ D))))).
% 3.45/1.76 thf(fact_250_process__term_Orel__transfer, axiom, (! [A:$tType,C:$tType,B:$tType,D:$tType,H2:$tType,F5:$tType,G2:$tType,E:$tType,S1a:(A > (E > $o)),S1c:(C > (G2 > $o)),S2a:(B > (F5 > $o)),S2c:(D > (H2 > $o))]: (((((((((bNF_rel_fun @ (A > (C > $o))) @ (E > (G2 > $o))) @ ((B > (D > $o)) > (((proces554692349s_term @ A) @ B) > (((proces554692349s_term @ C) @ D) > $o)))) @ ((F5 > (H2 > $o)) > (((proces554692349s_term @ E) @ F5) > (((proces554692349s_term @ G2) @ H2) > $o)))) @ ((((((bNF_rel_fun @ A) @ E) @ (C > $o)) @ (G2 > $o)) @ S1a) @ ((((((bNF_rel_fun @ C) @ G2) @ $o) @ $o) @ S1c) @ (^ [Y6:$o,Z:$o]: ((Y6 = Z)))))) @ ((((((bNF_rel_fun @ (B > (D > $o))) @ (F5 > (H2 > $o))) @ (((proces554692349s_term @ A) @ B) > (((proces554692349s_term @ C) @ D) > $o))) @ (((proces554692349s_term @ E) @ F5) > (((proces554692349s_term @ G2) @ H2) > $o))) @ ((((((bNF_rel_fun @ B) @ F5) @ (D > $o)) @ (H2 > $o)) @ S2a) @ ((((((bNF_rel_fun @ D) @ H2) @ $o) @ $o) @ S2c) @ (^ [Y6:$o,Z:$o]: ((Y6 = Z)))))) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ B)) @ ((proces554692349s_term @ E) @ F5)) @ (((proces554692349s_term @ C) @ D) > $o)) @ (((proces554692349s_term @ G2) @ H2) > $o)) @ ((((((proces2029722208s_term @ A) @ E) @ B) @ F5) @ S1a) @ S2a)) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ C) @ D)) @ ((proces554692349s_term @ G2) @ H2)) @ $o) @ $o) @ ((((((proces2029722208s_term @ C) @ G2) @ D) @ H2) @ S1c) @ S2c)) @ (^ [Y6:$o,Z:$o]: ((Y6 = Z))))))) @ ((((proces2029722208s_term @ A) @ C) @ B) @ D)) @ ((((proces2029722208s_term @ E) @ G2) @ F5) @ H2))))).
% 3.45/1.76 thf(fact_251_process__term_Omap__transfer, axiom, (! [A:$tType,C:$tType,B:$tType,D:$tType,L:$tType,J:$tType,K:$tType,I:$tType,R1b:(A > (I > $o)),S1d:(C > (K > $o)),R2b:(B > (J > $o)),S2d:(D > (L > $o))]: (((((((((bNF_rel_fun @ (A > C)) @ (I > K)) @ ((B > D) > (((proces554692349s_term @ A) @ B) > ((proces554692349s_term @ C) @ D)))) @ ((J > L) > (((proces554692349s_term @ I) @ J) > ((proces554692349s_term @ K) @ L)))) @ ((((((bNF_rel_fun @ A) @ I) @ C) @ K) @ R1b) @ S1d)) @ ((((((bNF_rel_fun @ (B > D)) @ (J > L)) @ (((proces554692349s_term @ A) @ B) > ((proces554692349s_term @ C) @ D))) @ (((proces554692349s_term @ I) @ J) > ((proces554692349s_term @ K) @ L))) @ ((((((bNF_rel_fun @ B) @ J) @ D) @ L) @ R2b) @ S2d)) @ ((((((bNF_rel_fun @ ((proces554692349s_term @ A) @ B)) @ ((proces554692349s_term @ I) @ J)) @ ((proces554692349s_term @ C) @ D)) @ ((proces554692349s_term @ K) @ L)) @ ((((((proces2029722208s_term @ A) @ I) @ B) @ J) @ R1b) @ R2b)) @ ((((((proces2029722208s_term @ C) @ K) @ D) @ L) @ S1d) @ S2d)))) @ ((((proces224683037s_term @ A) @ C) @ B) @ D)) @ ((((proces224683037s_term @ I) @ K) @ J) @ L))))).
% 3.45/1.76 thf(fact_252_process_Omap__transfer, axiom, (! [A:$tType,B:$tType,F5:$tType,E:$tType,Rb:(A > (E > $o)),Sd:(B > (F5 > $o))]: (((((((((bNF_rel_fun @ (A > B)) @ (E > F5)) @ ((proces634752977rocess @ A) > (proces634752977rocess @ B))) @ ((proces634752977rocess @ E) > (proces634752977rocess @ F5))) @ ((((((bNF_rel_fun @ A) @ E) @ B) @ F5) @ Rb) @ Sd)) @ ((((((bNF_rel_fun @ (proces634752977rocess @ A)) @ (proces634752977rocess @ E)) @ (proces634752977rocess @ B)) @ (proces634752977rocess @ F5)) @ (((proces749077512rocess @ A) @ E) @ Rb)) @ (((proces749077512rocess @ B) @ F5) @ Sd))) @ ((proces370407749rocess @ A) @ B)) @ ((proces370407749rocess @ E) @ F5))))).
% 3.45/1.76 thf(fact_253_process_Omap__disc__iff_I1_J, axiom, (! [B:$tType,A:$tType,F:(A > B),A2:(proces634752977rocess @ A)]: ((((proces10484146Action @ B) @ ((((proces370407749rocess @ A) @ B) @ F) @ A2)) = ((proces10484146Action @ A) @ A2))))).
% 3.45/1.76 thf(fact_254_process_Omap__disc__iff_I2_J, axiom, (! [B:$tType,A:$tType,F:(A > B),A2:(proces634752977rocess @ A)]: ((((proces401113213Choice @ B) @ ((((proces370407749rocess @ A) @ B) @ F) @ A2)) = ((proces401113213Choice @ A) @ A2))))).
% 3.45/1.76 thf(help_If_3_1_T, axiom, (! [P3:$o]: (((P3 = $true) | (P3 = $false))))).
% 3.45/1.76 thf(help_If_2_1_T, axiom, (! [A:$tType,X7:A,Y3:A]: ((((((if @ A) @ $false) @ X7) @ Y3) = Y3)))).
% 3.45/1.76 thf(help_If_1_1_T, axiom, (! [A:$tType,X7:A,Y3:A]: ((((((if @ A) @ $true) @ X7) @ Y3) = X7)))).
% 3.45/1.76 thf(conj_0, conjecture, ((a3 = a2) & (p2 = ((((proces1652378886lution @ b) @ a) @ sys) @ (((proces1062592052s_PROC @ a) @ b) @ pa))))).
% 3.45/1.76 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.sFYK9PDrEK/DTF2DTF15624.p
% 3.45/1.76 ------------------------
% 3.59/1.85 ---- Cleaned THF ---
% 3.59/1.85 thf(ty_t_Process__Mirabelle__xovoopgpgi_Oprocess__term,type,
% 3.59/1.85 proces554692349s_term: $tType > $tType > $tType ).
% 3.59/1.85
% 3.59/1.85 thf(ty_t_Process__Mirabelle__xovoopgpgi_Oprocess,type,
% 3.59/1.85 proces634752977rocess: $tType > $tType ).
% 3.59/1.85
% 3.59/1.85 thf(ty_t_Product__Type_Oprod,type,
% 3.59/1.85 product_prod: $tType > $tType > $tType ).
% 3.59/1.85
% 3.59/1.85 thf(ty_t_Set_Oset,type,
% 3.59/1.85 set: $tType > $tType ).
% 3.59/1.85
% 3.59/1.85 thf(ty_t_itself,type,
% 3.59/1.85 itself: $tType > $tType ).
% 3.59/1.85
% 3.59/1.85 thf(ty_tf_b,type,
% 3.59/1.85 b: $tType ).
% 3.59/1.85
% 3.59/1.85 thf(ty_tf_a,type,
% 3.59/1.85 a: $tType ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_BNF__Def_Orel__fun,type,
% 3.59/1.85 bNF_rel_fun:
% 3.59/1.85 !>[A: $tType,C: $tType,B: $tType,D: $tType] : ( ( A > C > $o ) > ( B > D > $o ) > ( A > B ) > ( C > D ) > $o ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_HOL_Oundefined,type,
% 3.59/1.85 undefined:
% 3.59/1.85 !>[A: $tType] : A ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_If,type,
% 3.59/1.85 if:
% 3.59/1.85 !>[A: $tType] : ( $o > A > A > A ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH1,type,
% 3.59/1.85 proces1239275103le_CH1:
% 3.59/1.85 !>[A: $tType,B: $tType] : ( ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > ( proces554692349s_term @ B @ A ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH1__rel,type,
% 3.59/1.85 proces1869379930H1_rel:
% 3.59/1.85 !>[A: $tType,B: $tType] : ( ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > $o ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH2,type,
% 3.59/1.85 proces1239275104le_CH2:
% 3.59/1.85 !>[A: $tType,B: $tType] : ( ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > ( proces554692349s_term @ B @ A ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCH2__rel,type,
% 3.59/1.85 proces93903513H2_rel:
% 3.59/1.85 !>[A: $tType,B: $tType] : ( ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > $o ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCONT,type,
% 3.59/1.85 proces126235999e_CONT:
% 3.59/1.85 !>[A: $tType,B: $tType] : ( ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > ( proces554692349s_term @ B @ A ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Process__Mirabelle__xovoopgpgi_OCONT__rel,type,
% 3.59/1.85 proces1004198490NT_rel:
% 3.59/1.85 !>[A: $tType,B: $tType] : ( ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) > $o ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Process__Mirabelle__xovoopgpgi_OPREF,type,
% 3.59/1.85 proces1708129104e_PREF:
% 3.59/1.85 !>[A: $tType,B: $tType,C: $tType] : ( ( A > ( proces554692349s_term @ B @ C ) ) > ( proces554692349s_term @ B @ A ) > B ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Process__Mirabelle__xovoopgpgi_OPREF__rel,type,
% 3.59/1.85 proces527360425EF_rel:
% 3.59/1.85 !>[A: $tType,B: $tType,C: $tType] : ( ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) > ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) > $o ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oguarded,type,
% 3.59/1.85 proces1121166967uarded:
% 3.59/1.85 !>[A: $tType,B: $tType,C: $tType] : ( ( A > ( proces554692349s_term @ B @ C ) ) > $o ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Process__Mirabelle__xovoopgpgi_OisACT,type,
% 3.59/1.85 proces687458811_isACT:
% 3.59/1.85 !>[A: $tType,B: $tType,C: $tType,D: $tType] : ( ( A > ( proces554692349s_term @ B @ C ) ) > ( proces554692349s_term @ D @ A ) > $o ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Process__Mirabelle__xovoopgpgi_OisACT__rel,type,
% 3.59/1.85 proces896239806CT_rel:
% 3.59/1.85 !>[A: $tType,B: $tType,C: $tType,D: $tType] : ( ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) > ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) > $o ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OAction,type,
% 3.59/1.85 proces1525233512Action:
% 3.59/1.85 !>[A: $tType] : ( A > ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OChoice,type,
% 3.59/1.85 proces1915862579Choice:
% 3.59/1.85 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Ocase__process,type,
% 3.59/1.85 proces1406508781rocess:
% 3.59/1.85 !>[A: $tType,B: $tType] : ( ( A > ( proces634752977rocess @ A ) > B ) > ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B ) > ( proces634752977rocess @ A ) > B ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Och1Of,type,
% 3.59/1.85 proces979765041_ch1Of:
% 3.59/1.85 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Och2Of,type,
% 3.59/1.85 proces988026546_ch2Of:
% 3.59/1.85 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OcontOf,type,
% 3.59/1.85 proces1778668539contOf:
% 3.59/1.85 !>[A: $tType] : ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Ocorec__process,type,
% 3.59/1.85 proces894737309rocess:
% 3.59/1.85 !>[C: $tType,A: $tType] : ( ( C > $o ) > ( C > A ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OisAction,type,
% 3.59/1.85 proces10484146Action:
% 3.59/1.85 !>[A: $tType] : ( ( proces634752977rocess @ A ) > $o ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OisChoice,type,
% 3.59/1.85 proces401113213Choice:
% 3.59/1.85 !>[A: $tType] : ( ( proces634752977rocess @ A ) > $o ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Omap__process,type,
% 3.59/1.85 proces370407749rocess:
% 3.59/1.85 !>[A: $tType,Aa: $tType] : ( ( A > Aa ) > ( proces634752977rocess @ A ) > ( proces634752977rocess @ Aa ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Opred__process,type,
% 3.59/1.85 proces1205983068rocess:
% 3.59/1.85 !>[A: $tType] : ( ( A > $o ) > ( proces634752977rocess @ A ) > $o ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_OprefOf,type,
% 3.59/1.85 proces745025900prefOf:
% 3.59/1.85 !>[A: $tType] : ( ( proces634752977rocess @ A ) > A ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess_Orel__process,type,
% 3.59/1.85 proces749077512rocess:
% 3.59/1.85 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( proces634752977rocess @ A ) > ( proces634752977rocess @ B ) > $o ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OACT,type,
% 3.59/1.85 proces1454156180ss_ACT:
% 3.59/1.85 !>[A: $tType,Pvar: $tType] : ( A > ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OCH,type,
% 3.59/1.85 proces89589571ess_CH:
% 3.59/1.85 !>[A: $tType,Pvar: $tType] : ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OPROC,type,
% 3.59/1.85 proces1062592052s_PROC:
% 3.59/1.85 !>[A: $tType,Pvar: $tType] : ( ( proces634752977rocess @ A ) > ( proces554692349s_term @ A @ Pvar ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_OVAR,type,
% 3.59/1.85 proces1627516585ss_VAR:
% 3.59/1.85 !>[Pvar: $tType,A: $tType] : ( Pvar > ( proces554692349s_term @ A @ Pvar ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Ocase__process__term,type,
% 3.59/1.85 proces460752237s_term:
% 3.59/1.85 !>[Pvar: $tType,B: $tType,A: $tType] : ( ( Pvar > B ) > ( ( proces634752977rocess @ A ) > B ) > ( A > ( proces554692349s_term @ A @ Pvar ) > B ) > ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B ) > ( proces554692349s_term @ A @ Pvar ) > B ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Omap__process__term,type,
% 3.59/1.85 proces224683037s_term:
% 3.59/1.85 !>[A: $tType,Aa: $tType,Pvar: $tType,Pvara: $tType] : ( ( A > Aa ) > ( Pvar > Pvara ) > ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ Aa @ Pvara ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Opred__process__term,type,
% 3.59/1.85 proces2118920028s_term:
% 3.59/1.85 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( B > $o ) > ( proces554692349s_term @ A @ B ) > $o ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Orec__process__term,type,
% 3.59/1.85 proces2117273769s_term:
% 3.59/1.85 !>[Pvar: $tType,D: $tType,A: $tType] : ( ( Pvar > D ) > ( ( proces634752977rocess @ A ) > D ) > ( A > ( proces554692349s_term @ A @ Pvar ) > D > D ) > ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Orel__process__term,type,
% 3.59/1.85 proces2029722208s_term:
% 3.59/1.85 !>[A: $tType,C: $tType,B: $tType,D: $tType] : ( ( A > C > $o ) > ( B > D > $o ) > ( proces554692349s_term @ A @ B ) > ( proces554692349s_term @ C @ D ) > $o ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Process__Mirabelle__xovoopgpgi_Oprocess__term_Oset2__process__term,type,
% 3.59/1.85 proces1493547885s_term:
% 3.59/1.85 !>[A: $tType,Pvar: $tType] : ( ( proces554692349s_term @ A @ Pvar ) > ( set @ Pvar ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Process__Mirabelle__xovoopgpgi_Osolution,type,
% 3.59/1.85 proces1652378886lution:
% 3.59/1.85 !>[A: $tType,B: $tType] : ( ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > ( proces634752977rocess @ B ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Product__Type_OPair,type,
% 3.59/1.85 product_Pair:
% 3.59/1.85 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Product__Type_Ocurry,type,
% 3.59/1.85 product_curry:
% 3.59/1.85 !>[A: $tType,B: $tType,C: $tType] : ( ( ( product_prod @ A @ B ) > C ) > A > B > C ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 3.59/1.85 produc2004651681e_prod:
% 3.59/1.85 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 3.59/1.85 product_rec_prod:
% 3.59/1.85 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Pure_Otype,type,
% 3.59/1.85 type:
% 3.59/1.85 !>[A: $tType] : ( itself @ A ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Relation_Oinv__image,type,
% 3.59/1.85 inv_image:
% 3.59/1.85 !>[B: $tType,A: $tType] : ( ( set @ ( product_prod @ B @ B ) ) > ( A > B ) > ( set @ ( product_prod @ A @ A ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Set_OCollect,type,
% 3.59/1.85 collect:
% 3.59/1.85 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Wellfounded_Oacc,type,
% 3.59/1.85 acc:
% 3.59/1.85 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ A ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Wellfounded_Oaccp,type,
% 3.59/1.85 accp:
% 3.59/1.85 !>[A: $tType] : ( ( A > A > $o ) > A > $o ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Wellfounded_Olex__prod,type,
% 3.59/1.85 lex_prod:
% 3.59/1.85 !>[A: $tType,B: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ B @ B ) ) > ( set @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Wfrec_Oadm__wf,type,
% 3.59/1.85 adm_wf:
% 3.59/1.85 !>[A: $tType,B: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( ( A > B ) > A > B ) > $o ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Wfrec_Ocut,type,
% 3.59/1.85 cut:
% 3.59/1.85 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ ( product_prod @ A @ A ) ) > A > A > B ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_Wfrec_Osame__fst,type,
% 3.59/1.85 same_fst:
% 3.59/1.85 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( A > ( set @ ( product_prod @ B @ B ) ) ) > ( set @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_c_member,type,
% 3.59/1.85 member:
% 3.59/1.85 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 3.59/1.85
% 3.59/1.85 thf(sy_v_a_H____,type,
% 3.59/1.85 a2: a ).
% 3.59/1.85
% 3.59/1.85 thf(sy_v_a____,type,
% 3.59/1.85 a3: a ).
% 3.59/1.85
% 3.59/1.85 thf(sy_v_p,type,
% 3.59/1.85 p: proces634752977rocess @ a ).
% 3.59/1.85
% 3.59/1.85 thf(sy_v_p_H____,type,
% 3.59/1.85 p2: proces634752977rocess @ a ).
% 3.59/1.85
% 3.59/1.85 thf(sy_v_pa____,type,
% 3.59/1.85 pa: proces634752977rocess @ a ).
% 3.59/1.85
% 3.59/1.85 thf(sy_v_q____,type,
% 3.59/1.85 q: proces634752977rocess @ a ).
% 3.59/1.85
% 3.59/1.85 thf(sy_v_sys,type,
% 3.59/1.85 sys: b > ( proces554692349s_term @ a @ b ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_0__092_060open_062q_A_061_Asolution_Asys_A_IPROC_Ap_J_092_060close_062,axiom,
% 3.59/1.85 ( q
% 3.59/1.85 = ( proces1652378886lution @ b @ a @ sys @ ( proces1062592052s_PROC @ a @ b @ p ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_1_process__term_Oinject_I2_J,axiom,
% 3.59/1.85 ! [Pvar: $tType,A: $tType,X2: proces634752977rocess @ A,Y2: proces634752977rocess @ A] :
% 3.59/1.85 ( ( ( proces1062592052s_PROC @ A @ Pvar @ X2 )
% 3.59/1.85 = ( proces1062592052s_PROC @ A @ Pvar @ Y2 ) )
% 3.59/1.85 = ( X2 = Y2 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_2_Action,axiom,
% 3.59/1.85 ( ( proces1525233512Action @ a @ a2 @ p2 )
% 3.59/1.85 = ( proces1652378886lution @ b @ a @ sys @ ( proces1062592052s_PROC @ a @ b @ ( proces1525233512Action @ a @ a3 @ pa ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_3__C0_C,axiom,
% 3.59/1.85 proces687458811_isACT @ b @ a @ b @ a @ sys @ ( proces1062592052s_PROC @ a @ b @ ( proces1525233512Action @ a @ a3 @ pa ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_4__092_060open_062solution_Asys_A_IPROC_A_IAction_Aa_Ap_J_J_A_061_AAction_A_IPREF_Asys_A_IPROC_A_IAction_Aa_Ap_J_J_J_A_Isolution_Asys_A_ICONT_Asys_A_IPROC_A_IAction_Aa_Ap_J_J_J_J_092_060close_062,axiom,
% 3.59/1.85 ( ( proces1652378886lution @ b @ a @ sys @ ( proces1062592052s_PROC @ a @ b @ ( proces1525233512Action @ a @ a3 @ pa ) ) )
% 3.59/1.85 = ( proces1525233512Action @ a @ ( proces1708129104e_PREF @ b @ a @ b @ sys @ ( proces1062592052s_PROC @ a @ b @ ( proces1525233512Action @ a @ a3 @ pa ) ) ) @ ( proces1652378886lution @ b @ a @ sys @ ( proces126235999e_CONT @ b @ a @ sys @ ( proces1062592052s_PROC @ a @ b @ ( proces1525233512Action @ a @ a3 @ pa ) ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_5_process__term_Osimps_I22_J,axiom,
% 3.59/1.85 ! [Pvar: $tType,D: $tType,A: $tType,F1: Pvar > D,F2: ( proces634752977rocess @ A ) > D,F3: A > ( proces554692349s_term @ A @ Pvar ) > D > D,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D,X2: proces634752977rocess @ A] :
% 3.59/1.85 ( ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) )
% 3.59/1.85 = ( F2 @ X2 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_6_process__term_Osimps_I18_J,axiom,
% 3.59/1.85 ! [Pvar: $tType,B: $tType,A: $tType,F1: Pvar > B,F2: ( proces634752977rocess @ A ) > B,F3: A > ( proces554692349s_term @ A @ Pvar ) > B,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B,X2: proces634752977rocess @ A] :
% 3.59/1.85 ( ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) )
% 3.59/1.85 = ( F2 @ X2 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_7_process__term_Odistinct_I7_J,axiom,
% 3.59/1.85 ! [Pvar: $tType,A: $tType,X2: proces634752977rocess @ A,X31: A,X32: proces554692349s_term @ A @ Pvar] :
% 3.59/1.85 ( ( proces1062592052s_PROC @ A @ Pvar @ X2 )
% 3.59/1.85 != ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_8_process__term_Odistinct_I9_J,axiom,
% 3.59/1.85 ! [Pvar: $tType,A: $tType,X2: proces634752977rocess @ A,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
% 3.59/1.85 ( ( proces1062592052s_PROC @ A @ Pvar @ X2 )
% 3.59/1.85 != ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_9_process__term_Odistinct_I1_J,axiom,
% 3.59/1.85 ! [Pvar: $tType,A: $tType,X1: Pvar,X2: proces634752977rocess @ A] :
% 3.59/1.85 ( ( proces1627516585ss_VAR @ Pvar @ A @ X1 )
% 3.59/1.85 != ( proces1062592052s_PROC @ A @ Pvar @ X2 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_10_process_Ocase__distrib,axiom,
% 3.59/1.85 ! [B: $tType,C: $tType,A: $tType,H: B > C,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process: proces634752977rocess @ A] :
% 3.59/1.85 ( ( H @ ( proces1406508781rocess @ A @ B @ F1 @ F2 @ Process ) )
% 3.59/1.85 = ( proces1406508781rocess @ A @ C
% 3.59/1.85 @ ^ [X12: A,X22: proces634752977rocess @ A] : ( H @ ( F1 @ X12 @ X22 ) )
% 3.59/1.85 @ ^ [X12: proces634752977rocess @ A,X22: proces634752977rocess @ A] : ( H @ ( F2 @ X12 @ X22 ) )
% 3.59/1.85 @ Process ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_11_process__term_Ocase__distrib,axiom,
% 3.59/1.85 ! [B: $tType,C: $tType,Pvar: $tType,A: $tType,H: B > C,F1: Pvar > B,F2: ( proces634752977rocess @ A ) > B,F3: A > ( proces554692349s_term @ A @ Pvar ) > B,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B,Process_term: proces554692349s_term @ A @ Pvar] :
% 3.59/1.85 ( ( H @ ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ Process_term ) )
% 3.59/1.85 = ( proces460752237s_term @ Pvar @ C @ A
% 3.59/1.85 @ ^ [X: Pvar] : ( H @ ( F1 @ X ) )
% 3.59/1.85 @ ^ [X: proces634752977rocess @ A] : ( H @ ( F2 @ X ) )
% 3.59/1.85 @ ^ [X12: A,X22: proces554692349s_term @ A @ Pvar] : ( H @ ( F3 @ X12 @ X22 ) )
% 3.59/1.85 @ ^ [X12: proces554692349s_term @ A @ Pvar,X22: proces554692349s_term @ A @ Pvar] : ( H @ ( F4 @ X12 @ X22 ) )
% 3.59/1.85 @ Process_term ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_12_solution__VAR,axiom,
% 3.59/1.85 ! [B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X3: A] :
% 3.59/1.85 ( ( proces1121166967uarded @ A @ B @ A @ Sys )
% 3.59/1.85 => ( ( proces1652378886lution @ A @ B @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X3 ) )
% 3.59/1.85 = ( proces1652378886lution @ A @ B @ Sys @ ( Sys @ X3 ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_13_PREF_Osimps_I2_J,axiom,
% 3.59/1.85 ! [A: $tType,C: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ C ),P: proces634752977rocess @ B] :
% 3.59/1.85 ( ( proces1708129104e_PREF @ A @ B @ C @ Sys @ ( proces1062592052s_PROC @ B @ A @ P ) )
% 3.59/1.85 = ( proces745025900prefOf @ B @ P ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_14_process__term_Opred__inject_I2_J,axiom,
% 3.59/1.85 ! [Pvar: $tType,A: $tType,P1: A > $o,P2: Pvar > $o,A2: proces634752977rocess @ A] :
% 3.59/1.85 ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ ( proces1062592052s_PROC @ A @ Pvar @ A2 ) )
% 3.59/1.85 = ( proces1205983068rocess @ A @ P1 @ A2 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_15_process__term_Oinject_I1_J,axiom,
% 3.59/1.85 ! [A: $tType,Pvar: $tType,X1: Pvar,Y1: Pvar] :
% 3.59/1.85 ( ( ( proces1627516585ss_VAR @ Pvar @ A @ X1 )
% 3.59/1.85 = ( proces1627516585ss_VAR @ Pvar @ A @ Y1 ) )
% 3.59/1.85 = ( X1 = Y1 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_16_process__term_Oinject_I4_J,axiom,
% 3.59/1.85 ! [Pvar: $tType,A: $tType,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar,Y41: proces554692349s_term @ A @ Pvar,Y42: proces554692349s_term @ A @ Pvar] :
% 3.59/1.85 ( ( ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 )
% 3.59/1.85 = ( proces89589571ess_CH @ A @ Pvar @ Y41 @ Y42 ) )
% 3.59/1.85 = ( ( X41 = Y41 )
% 3.59/1.85 & ( X42 = Y42 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_17_process__term_Oinject_I3_J,axiom,
% 3.59/1.85 ! [Pvar: $tType,A: $tType,X31: A,X32: proces554692349s_term @ A @ Pvar,Y31: A,Y32: proces554692349s_term @ A @ Pvar] :
% 3.59/1.85 ( ( ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 )
% 3.59/1.85 = ( proces1454156180ss_ACT @ A @ Pvar @ Y31 @ Y32 ) )
% 3.59/1.85 = ( ( X31 = Y31 )
% 3.59/1.85 & ( X32 = Y32 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_18_process_Oinject_I1_J,axiom,
% 3.59/1.85 ! [A: $tType,X11: A,X122: proces634752977rocess @ A,Y11: A,Y12: proces634752977rocess @ A] :
% 3.59/1.85 ( ( ( proces1525233512Action @ A @ X11 @ X122 )
% 3.59/1.85 = ( proces1525233512Action @ A @ Y11 @ Y12 ) )
% 3.59/1.85 = ( ( X11 = Y11 )
% 3.59/1.85 & ( X122 = Y12 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_19_process__term_Opred__inject_I1_J,axiom,
% 3.59/1.85 ! [A: $tType,Pvar: $tType,P1: A > $o,P2: Pvar > $o,A2: Pvar] :
% 3.59/1.85 ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ ( proces1627516585ss_VAR @ Pvar @ A @ A2 ) )
% 3.59/1.85 = ( P2 @ A2 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_20_process__term_Opred__inject_I4_J,axiom,
% 3.59/1.85 ! [Pvar: $tType,A: $tType,P1: A > $o,P2: Pvar > $o,A2: proces554692349s_term @ A @ Pvar,Aa2: proces554692349s_term @ A @ Pvar] :
% 3.59/1.85 ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ ( proces89589571ess_CH @ A @ Pvar @ A2 @ Aa2 ) )
% 3.59/1.85 = ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ A2 )
% 3.59/1.85 & ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ Aa2 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_21_process__term_Opred__inject_I3_J,axiom,
% 3.59/1.85 ! [Pvar: $tType,A: $tType,P1: A > $o,P2: Pvar > $o,A2: A,Aa2: proces554692349s_term @ A @ Pvar] :
% 3.59/1.85 ( ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ ( proces1454156180ss_ACT @ A @ Pvar @ A2 @ Aa2 ) )
% 3.59/1.85 = ( ( P1 @ A2 )
% 3.59/1.85 & ( proces2118920028s_term @ A @ Pvar @ P1 @ P2 @ Aa2 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_22_process_Opred__inject_I1_J,axiom,
% 3.59/1.85 ! [A: $tType,P3: A > $o,A2: A,Aa2: proces634752977rocess @ A] :
% 3.59/1.85 ( ( proces1205983068rocess @ A @ P3 @ ( proces1525233512Action @ A @ A2 @ Aa2 ) )
% 3.59/1.85 = ( ( P3 @ A2 )
% 3.59/1.85 & ( proces1205983068rocess @ A @ P3 @ Aa2 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_23_CONT_Osimps_I3_J,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),A2: B,T2: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( ( proces126235999e_CONT @ A @ B @ Sys @ ( proces1454156180ss_ACT @ B @ A @ A2 @ T2 ) )
% 3.59/1.85 = T2 ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_24_PREF_Osimps_I3_J,axiom,
% 3.59/1.85 ! [A: $tType,C: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ C ),A2: B,T2: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( ( proces1708129104e_PREF @ A @ B @ C @ Sys @ ( proces1454156180ss_ACT @ B @ A @ A2 @ T2 ) )
% 3.59/1.85 = A2 ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_25_isACT_Osimps_I4_J,axiom,
% 3.59/1.85 ! [B: $tType,C: $tType,A: $tType,D: $tType,Sys: A > ( proces554692349s_term @ B @ C ),T1: proces554692349s_term @ D @ A,T22: proces554692349s_term @ D @ A] :
% 3.59/1.85 ~ ( proces687458811_isACT @ A @ B @ C @ D @ Sys @ ( proces89589571ess_CH @ D @ A @ T1 @ T22 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_26_isACT_Osimps_I3_J,axiom,
% 3.59/1.85 ! [B: $tType,C: $tType,A: $tType,D: $tType,Sys: A > ( proces554692349s_term @ B @ C ),A2: D,T2: proces554692349s_term @ D @ A] : ( proces687458811_isACT @ A @ B @ C @ D @ Sys @ ( proces1454156180ss_ACT @ D @ A @ A2 @ T2 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_27_process_Osel_I1_J,axiom,
% 3.59/1.85 ! [A: $tType,X11: A,X122: proces634752977rocess @ A] :
% 3.59/1.85 ( ( proces745025900prefOf @ A @ ( proces1525233512Action @ A @ X11 @ X122 ) )
% 3.59/1.85 = X11 ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_28_solution_Octr_I1_J,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 3.59/1.85 => ( ( proces1652378886lution @ A @ B @ Sys @ T2 )
% 3.59/1.85 = ( proces1525233512Action @ B @ ( proces1708129104e_PREF @ A @ B @ A @ Sys @ T2 ) @ ( proces1652378886lution @ A @ B @ Sys @ ( proces126235999e_CONT @ A @ B @ Sys @ T2 ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_29_process_Osimps_I5_J,axiom,
% 3.59/1.85 ! [B: $tType,A: $tType,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,X11: A,X122: proces634752977rocess @ A] :
% 3.59/1.85 ( ( proces1406508781rocess @ A @ B @ F1 @ F2 @ ( proces1525233512Action @ A @ X11 @ X122 ) )
% 3.59/1.85 = ( F1 @ X11 @ X122 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_30_process__term_Osimps_I24_J,axiom,
% 3.59/1.85 ! [D: $tType,Pvar: $tType,A: $tType,F1: Pvar > D,F2: ( proces634752977rocess @ A ) > D,F3: A > ( proces554692349s_term @ A @ Pvar ) > D > D,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
% 3.59/1.85 ( ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) )
% 3.59/1.85 = ( F4 @ X41 @ X42 @ ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ X41 ) @ ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ X42 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_31_process__term_Osimps_I23_J,axiom,
% 3.59/1.85 ! [D: $tType,Pvar: $tType,A: $tType,F1: Pvar > D,F2: ( proces634752977rocess @ A ) > D,F3: A > ( proces554692349s_term @ A @ Pvar ) > D > D,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D,X31: A,X32: proces554692349s_term @ A @ Pvar] :
% 3.59/1.85 ( ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) )
% 3.59/1.85 = ( F3 @ X31 @ X32 @ ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ X32 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_32_process__term_Osimps_I21_J,axiom,
% 3.59/1.85 ! [A: $tType,D: $tType,Pvar: $tType,F1: Pvar > D,F2: ( proces634752977rocess @ A ) > D,F3: A > ( proces554692349s_term @ A @ Pvar ) > D > D,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D,X1: Pvar] :
% 3.59/1.85 ( ( proces2117273769s_term @ Pvar @ D @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) )
% 3.59/1.85 = ( F1 @ X1 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_33_process__term_Osimps_I20_J,axiom,
% 3.59/1.85 ! [B: $tType,Pvar: $tType,A: $tType,F1: Pvar > B,F2: ( proces634752977rocess @ A ) > B,F3: A > ( proces554692349s_term @ A @ Pvar ) > B,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
% 3.59/1.85 ( ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) )
% 3.59/1.85 = ( F4 @ X41 @ X42 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_34_process__term_Osimps_I19_J,axiom,
% 3.59/1.85 ! [B: $tType,Pvar: $tType,A: $tType,F1: Pvar > B,F2: ( proces634752977rocess @ A ) > B,F3: A > ( proces554692349s_term @ A @ Pvar ) > B,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B,X31: A,X32: proces554692349s_term @ A @ Pvar] :
% 3.59/1.85 ( ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) )
% 3.59/1.85 = ( F3 @ X31 @ X32 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_35_process__term_Osimps_I17_J,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,Pvar: $tType,F1: Pvar > B,F2: ( proces634752977rocess @ A ) > B,F3: A > ( proces554692349s_term @ A @ Pvar ) > B,F4: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > B,X1: Pvar] :
% 3.59/1.85 ( ( proces460752237s_term @ Pvar @ B @ A @ F1 @ F2 @ F3 @ F4 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) )
% 3.59/1.85 = ( F1 @ X1 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_36_process__term_Odistinct_I11_J,axiom,
% 3.59/1.85 ! [Pvar: $tType,A: $tType,X31: A,X32: proces554692349s_term @ A @ Pvar,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
% 3.59/1.85 ( ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 )
% 3.59/1.85 != ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_37_process__term_Odistinct_I5_J,axiom,
% 3.59/1.85 ! [Pvar: $tType,A: $tType,X1: Pvar,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar] :
% 3.59/1.85 ( ( proces1627516585ss_VAR @ Pvar @ A @ X1 )
% 3.59/1.85 != ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_38_process__term_Odistinct_I3_J,axiom,
% 3.59/1.85 ! [Pvar: $tType,A: $tType,X1: Pvar,X31: A,X32: proces554692349s_term @ A @ Pvar] :
% 3.59/1.85 ( ( proces1627516585ss_VAR @ Pvar @ A @ X1 )
% 3.59/1.85 != ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_39_isACT__VAR,axiom,
% 3.59/1.85 ! [C: $tType,B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X3: A] :
% 3.59/1.85 ( ( proces1121166967uarded @ A @ B @ A @ Sys )
% 3.59/1.85 => ( ( proces687458811_isACT @ A @ B @ A @ C @ Sys @ ( proces1627516585ss_VAR @ A @ C @ X3 ) )
% 3.59/1.85 = ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ ( Sys @ X3 ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_40_CH2_Oinduct,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,P3: ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > $o,A0: A > ( proces554692349s_term @ B @ A ),A1: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),X4: A] : ( P3 @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 3.59/1.85 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),P4: proces634752977rocess @ B] : ( P3 @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 3.59/1.85 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] : ( P3 @ Sys2 @ ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
% 3.59/1.85 => ( ! [A3: A > ( proces554692349s_term @ B @ A ),V: B,Va: proces554692349s_term @ B @ A] : ( P3 @ A3 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
% 3.59/1.85 => ( P3 @ A0 @ A1 ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_41_CONT_Oinduct,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,P3: ( A > ( proces554692349s_term @ B @ A ) ) > ( proces554692349s_term @ B @ A ) > $o,A0: A > ( proces554692349s_term @ B @ A ),A1: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),X4: A] : ( P3 @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 3.59/1.85 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),P4: proces634752977rocess @ B] : ( P3 @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 3.59/1.85 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),A3: B,T3: proces554692349s_term @ B @ A] : ( P3 @ Sys2 @ ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) )
% 3.59/1.85 => ( ! [A3: A > ( proces554692349s_term @ B @ A ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] : ( P3 @ A3 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 3.59/1.85 => ( P3 @ A0 @ A1 ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_42_PREF_Oinduct,axiom,
% 3.59/1.85 ! [C: $tType,A: $tType,B: $tType,P3: ( A > ( proces554692349s_term @ B @ C ) ) > ( proces554692349s_term @ B @ A ) > $o,A0: A > ( proces554692349s_term @ B @ C ),A1: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),X4: A] : ( P3 @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 3.59/1.85 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),P4: proces634752977rocess @ B] : ( P3 @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 3.59/1.85 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),A3: B,T3: proces554692349s_term @ B @ A] : ( P3 @ Sys2 @ ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) )
% 3.59/1.85 => ( ! [A3: A > ( proces554692349s_term @ B @ C ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] : ( P3 @ A3 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 3.59/1.85 => ( P3 @ A0 @ A1 ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_43_guarded__def,axiom,
% 3.59/1.85 ! [C: $tType,B: $tType,A: $tType] :
% 3.59/1.85 ( ( proces1121166967uarded @ A @ B @ C )
% 3.59/1.85 = ( ^ [Sys3: A > ( proces554692349s_term @ B @ C )] :
% 3.59/1.85 ! [X5: A,Y: C] :
% 3.59/1.85 ( ( Sys3 @ X5 )
% 3.59/1.85 != ( proces1627516585ss_VAR @ C @ B @ Y ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_44_isACT_Oinduct,axiom,
% 3.59/1.85 ! [B: $tType,C: $tType,A: $tType,D: $tType,P3: ( A > ( proces554692349s_term @ B @ C ) ) > ( proces554692349s_term @ D @ A ) > $o,A0: A > ( proces554692349s_term @ B @ C ),A1: proces554692349s_term @ D @ A] :
% 3.59/1.85 ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),X4: A] : ( P3 @ Sys2 @ ( proces1627516585ss_VAR @ A @ D @ X4 ) )
% 3.59/1.85 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),P4: proces634752977rocess @ D] : ( P3 @ Sys2 @ ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 3.59/1.85 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),A3: D,T3: proces554692349s_term @ D @ A] : ( P3 @ Sys2 @ ( proces1454156180ss_ACT @ D @ A @ A3 @ T3 ) )
% 3.59/1.85 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] : ( P3 @ Sys2 @ ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) )
% 3.59/1.85 => ( P3 @ A0 @ A1 ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_45_mem__Collect__eq,axiom,
% 3.59/1.85 ! [A: $tType,A2: A,P3: A > $o] :
% 3.59/1.85 ( ( member @ A @ A2 @ ( collect @ A @ P3 ) )
% 3.59/1.85 = ( P3 @ A2 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_46_Collect__mem__eq,axiom,
% 3.59/1.85 ! [A: $tType,A4: set @ A] :
% 3.59/1.85 ( ( collect @ A
% 3.59/1.85 @ ^ [X: A] : ( member @ A @ X @ A4 ) )
% 3.59/1.85 = A4 ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_47_Collect__cong,axiom,
% 3.59/1.85 ! [A: $tType,P3: A > $o,Q: A > $o] :
% 3.59/1.85 ( ! [X6: A] :
% 3.59/1.85 ( ( P3 @ X6 )
% 3.59/1.85 = ( Q @ X6 ) )
% 3.59/1.85 => ( ( collect @ A @ P3 )
% 3.59/1.85 = ( collect @ A @ Q ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_48_ext,axiom,
% 3.59/1.85 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 3.59/1.85 ( ! [X6: A] :
% 3.59/1.85 ( ( F @ X6 )
% 3.59/1.85 = ( G @ X6 ) )
% 3.59/1.85 => ( F = G ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_49_process__term_Oinduct,axiom,
% 3.59/1.85 ! [Pvar: $tType,A: $tType,P3: ( proces554692349s_term @ A @ Pvar ) > $o,Process_term: proces554692349s_term @ A @ Pvar] :
% 3.59/1.85 ( ! [X6: Pvar] : ( P3 @ ( proces1627516585ss_VAR @ Pvar @ A @ X6 ) )
% 3.59/1.85 => ( ! [X6: proces634752977rocess @ A] : ( P3 @ ( proces1062592052s_PROC @ A @ Pvar @ X6 ) )
% 3.59/1.85 => ( ! [X1a: A,X2a: proces554692349s_term @ A @ Pvar] :
% 3.59/1.85 ( ( P3 @ X2a )
% 3.59/1.85 => ( P3 @ ( proces1454156180ss_ACT @ A @ Pvar @ X1a @ X2a ) ) )
% 3.59/1.85 => ( ! [X1a: proces554692349s_term @ A @ Pvar,X2a: proces554692349s_term @ A @ Pvar] :
% 3.59/1.85 ( ( P3 @ X1a )
% 3.59/1.85 => ( ( P3 @ X2a )
% 3.59/1.85 => ( P3 @ ( proces89589571ess_CH @ A @ Pvar @ X1a @ X2a ) ) ) )
% 3.59/1.85 => ( P3 @ Process_term ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_50_process__term_Oexhaust,axiom,
% 3.59/1.85 ! [Pvar: $tType,A: $tType,Y3: proces554692349s_term @ A @ Pvar] :
% 3.59/1.85 ( ! [X13: Pvar] :
% 3.59/1.85 ( Y3
% 3.59/1.85 != ( proces1627516585ss_VAR @ Pvar @ A @ X13 ) )
% 3.59/1.85 => ( ! [X23: proces634752977rocess @ A] :
% 3.59/1.85 ( Y3
% 3.59/1.85 != ( proces1062592052s_PROC @ A @ Pvar @ X23 ) )
% 3.59/1.85 => ( ! [X312: A,X322: proces554692349s_term @ A @ Pvar] :
% 3.59/1.85 ( Y3
% 3.59/1.85 != ( proces1454156180ss_ACT @ A @ Pvar @ X312 @ X322 ) )
% 3.59/1.85 => ~ ! [X412: proces554692349s_term @ A @ Pvar,X422: proces554692349s_term @ A @ Pvar] :
% 3.59/1.85 ( Y3
% 3.59/1.85 != ( proces89589571ess_CH @ A @ Pvar @ X412 @ X422 ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_51_solution_Osimps_I3_J,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 3.59/1.85 => ( ( proces745025900prefOf @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 3.59/1.85 = ( proces1708129104e_PREF @ A @ B @ A @ Sys @ T2 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_52_process__term_Opred__True,axiom,
% 3.59/1.85 ! [B: $tType,A: $tType] :
% 3.59/1.85 ( ( proces2118920028s_term @ A @ B
% 3.59/1.85 @ ^ [Uu: A] : $true
% 3.59/1.85 @ ^ [Uu: B] : $true )
% 3.59/1.85 = ( ^ [Uu: proces554692349s_term @ A @ B] : $true ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_53_process_Opred__True,axiom,
% 3.59/1.85 ! [A: $tType] :
% 3.59/1.85 ( ( proces1205983068rocess @ A
% 3.59/1.85 @ ^ [Uu: A] : $true )
% 3.59/1.85 = ( ^ [Uu: proces634752977rocess @ A] : $true ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_54_PREF_Oelims,axiom,
% 3.59/1.85 ! [A: $tType,C: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ B @ A,Y3: B] :
% 3.59/1.85 ( ( ( proces1708129104e_PREF @ A @ B @ C @ X7 @ Xa )
% 3.59/1.85 = Y3 )
% 3.59/1.85 => ( ! [X4: A] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 3.59/1.85 => ( Y3
% 3.59/1.85 != ( proces460752237s_term @ C @ B @ B
% 3.59/1.85 @ ^ [Aa3: C] : ( undefined @ B )
% 3.59/1.85 @ ( proces745025900prefOf @ B )
% 3.59/1.85 @ ^ [A5: B,T4: proces554692349s_term @ B @ C] : A5
% 3.59/1.85 @ ^ [Aa3: proces554692349s_term @ B @ C,Ab: proces554692349s_term @ B @ C] : ( undefined @ B )
% 3.59/1.85 @ ( X7 @ X4 ) ) ) )
% 3.59/1.85 => ( ! [P4: proces634752977rocess @ B] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 3.59/1.85 => ( Y3
% 3.59/1.85 != ( proces745025900prefOf @ B @ P4 ) ) )
% 3.59/1.85 => ( ! [A3: B] :
% 3.59/1.85 ( ? [T3: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( Xa
% 3.59/1.85 = ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) )
% 3.59/1.85 => ( Y3 != A3 ) )
% 3.59/1.85 => ~ ( ? [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( Xa
% 3.59/1.85 = ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 3.59/1.85 => ( Y3
% 3.59/1.85 != ( undefined @ B ) ) ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_55_isACT_Oelims_I1_J,axiom,
% 3.59/1.85 ! [D: $tType,A: $tType,B: $tType,C: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A,Y3: $o] :
% 3.59/1.85 ( ( ( proces687458811_isACT @ A @ B @ C @ D @ X7 @ Xa )
% 3.59/1.85 = Y3 )
% 3.59/1.85 => ( ! [X4: A] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces1627516585ss_VAR @ A @ D @ X4 ) )
% 3.59/1.85 => ( Y3
% 3.59/1.85 = ( ~ ( proces460752237s_term @ C @ $o @ B
% 3.59/1.85 @ ^ [Pvar2: C] : $false
% 3.59/1.85 @ ( proces10484146Action @ B )
% 3.59/1.85 @ ^ [A5: B,T4: proces554692349s_term @ B @ C] : $true
% 3.59/1.85 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 3.59/1.85 @ ( X7 @ X4 ) ) ) ) )
% 3.59/1.85 => ( ! [P4: proces634752977rocess @ D] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 3.59/1.85 => ( Y3
% 3.59/1.85 = ( ~ ( proces10484146Action @ D @ P4 ) ) ) )
% 3.59/1.85 => ( ( ? [A3: D,T3: proces554692349s_term @ D @ A] :
% 3.59/1.85 ( Xa
% 3.59/1.85 = ( proces1454156180ss_ACT @ D @ A @ A3 @ T3 ) )
% 3.59/1.85 => ~ Y3 )
% 3.59/1.85 => ~ ( ? [T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
% 3.59/1.85 ( Xa
% 3.59/1.85 = ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) )
% 3.59/1.85 => Y3 ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_56_PREF_Osimps_I1_J,axiom,
% 3.59/1.85 ! [B: $tType,C: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ C ),X3: A] :
% 3.59/1.85 ( ( proces1708129104e_PREF @ A @ B @ C @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X3 ) )
% 3.59/1.85 = ( proces460752237s_term @ C @ B @ B
% 3.59/1.85 @ ^ [Aa3: C] : ( undefined @ B )
% 3.59/1.85 @ ( proces745025900prefOf @ B )
% 3.59/1.85 @ ^ [A5: B,T4: proces554692349s_term @ B @ C] : A5
% 3.59/1.85 @ ^ [Aa3: proces554692349s_term @ B @ C,Ab: proces554692349s_term @ B @ C] : ( undefined @ B )
% 3.59/1.85 @ ( Sys @ X3 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_57_isACT_Oelims_I2_J,axiom,
% 3.59/1.85 ! [C: $tType,B: $tType,A: $tType,D: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A] :
% 3.59/1.85 ( ( proces687458811_isACT @ A @ B @ C @ D @ X7 @ Xa )
% 3.59/1.85 => ( ! [X4: A] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces1627516585ss_VAR @ A @ D @ X4 ) )
% 3.59/1.85 => ~ ( proces460752237s_term @ C @ $o @ B
% 3.59/1.85 @ ^ [Pvar2: C] : $false
% 3.59/1.85 @ ( proces10484146Action @ B )
% 3.59/1.85 @ ^ [A5: B,T4: proces554692349s_term @ B @ C] : $true
% 3.59/1.85 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 3.59/1.85 @ ( X7 @ X4 ) ) )
% 3.59/1.85 => ( ! [P4: proces634752977rocess @ D] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 3.59/1.85 => ~ ( proces10484146Action @ D @ P4 ) )
% 3.59/1.85 => ~ ! [A3: D,T3: proces554692349s_term @ D @ A] :
% 3.59/1.85 ( Xa
% 3.59/1.85 != ( proces1454156180ss_ACT @ D @ A @ A3 @ T3 ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_58_isACT_Oelims_I3_J,axiom,
% 3.59/1.85 ! [C: $tType,B: $tType,A: $tType,D: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A] :
% 3.59/1.85 ( ~ ( proces687458811_isACT @ A @ B @ C @ D @ X7 @ Xa )
% 3.59/1.85 => ( ! [X4: A] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces1627516585ss_VAR @ A @ D @ X4 ) )
% 3.59/1.85 => ( proces460752237s_term @ C @ $o @ B
% 3.59/1.85 @ ^ [Pvar2: C] : $false
% 3.59/1.85 @ ( proces10484146Action @ B )
% 3.59/1.85 @ ^ [A5: B,T4: proces554692349s_term @ B @ C] : $true
% 3.59/1.85 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 3.59/1.85 @ ( X7 @ X4 ) ) )
% 3.59/1.85 => ( ! [P4: proces634752977rocess @ D] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 3.59/1.85 => ( proces10484146Action @ D @ P4 ) )
% 3.59/1.85 => ~ ! [T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
% 3.59/1.85 ( Xa
% 3.59/1.85 != ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_59_solution_Osimps_I4_J,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 3.59/1.85 => ( ( proces1778668539contOf @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 3.59/1.85 = ( proces1652378886lution @ A @ B @ Sys @ ( proces126235999e_CONT @ A @ B @ Sys @ T2 ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_60_CH2_Ocases,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,X7: product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A )] :
% 3.59/1.85 ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),X4: A] :
% 3.59/1.85 ( X7
% 3.59/1.85 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) ) )
% 3.59/1.85 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),P4: proces634752977rocess @ B] :
% 3.59/1.85 ( X7
% 3.59/1.85 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) )
% 3.59/1.85 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( X7
% 3.59/1.85 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) ) )
% 3.59/1.85 => ~ ! [A3: A > ( proces554692349s_term @ B @ A ),V: B,Va: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( X7
% 3.59/1.85 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ A3 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_61_CONT_Ocases,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,X7: product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A )] :
% 3.59/1.85 ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),X4: A] :
% 3.59/1.85 ( X7
% 3.59/1.85 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) ) )
% 3.59/1.85 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),P4: proces634752977rocess @ B] :
% 3.59/1.85 ( X7
% 3.59/1.85 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) )
% 3.59/1.85 => ( ! [Sys2: A > ( proces554692349s_term @ B @ A ),A3: B,T3: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( X7
% 3.59/1.85 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) ) )
% 3.59/1.85 => ~ ! [A3: A > ( proces554692349s_term @ B @ A ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( X7
% 3.59/1.85 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ A3 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_62_PREF_Ocases,axiom,
% 3.59/1.85 ! [C: $tType,A: $tType,B: $tType,X7: product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A )] :
% 3.59/1.85 ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),X4: A] :
% 3.59/1.85 ( X7
% 3.59/1.85 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) ) )
% 3.59/1.85 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),P4: proces634752977rocess @ B] :
% 3.59/1.85 ( X7
% 3.59/1.85 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) )
% 3.59/1.85 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),A3: B,T3: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( X7
% 3.59/1.85 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ Sys2 @ ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) ) )
% 3.59/1.85 => ~ ! [A3: A > ( proces554692349s_term @ B @ C ),V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( X7
% 3.59/1.85 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ A3 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_63_isACT_Ocases,axiom,
% 3.59/1.85 ! [B: $tType,C: $tType,A: $tType,D: $tType,X7: product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A )] :
% 3.59/1.85 ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),X4: A] :
% 3.59/1.85 ( X7
% 3.59/1.85 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys2 @ ( proces1627516585ss_VAR @ A @ D @ X4 ) ) )
% 3.59/1.85 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),P4: proces634752977rocess @ D] :
% 3.59/1.85 ( X7
% 3.59/1.85 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys2 @ ( proces1062592052s_PROC @ D @ A @ P4 ) ) )
% 3.59/1.85 => ( ! [Sys2: A > ( proces554692349s_term @ B @ C ),A3: D,T3: proces554692349s_term @ D @ A] :
% 3.59/1.85 ( X7
% 3.59/1.85 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys2 @ ( proces1454156180ss_ACT @ D @ A @ A3 @ T3 ) ) )
% 3.59/1.85 => ~ ! [Sys2: A > ( proces554692349s_term @ B @ C ),T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
% 3.59/1.85 ( X7
% 3.59/1.85 != ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ Sys2 @ ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_64_solution_Odisc__iff_I1_J,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( ( proces10484146Action @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 3.59/1.85 = ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_65_process_Ocollapse_I1_J,axiom,
% 3.59/1.85 ! [A: $tType,Process: proces634752977rocess @ A] :
% 3.59/1.85 ( ( proces10484146Action @ A @ Process )
% 3.59/1.85 => ( ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) )
% 3.59/1.85 = Process ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_66_contOf__def,axiom,
% 3.59/1.85 ! [A: $tType] :
% 3.59/1.85 ( ( proces1778668539contOf @ A )
% 3.59/1.85 = ( proces1406508781rocess @ A @ ( proces634752977rocess @ A )
% 3.59/1.85 @ ^ [X112: A,X123: proces634752977rocess @ A] : X123
% 3.59/1.85 @ ^ [Uu2: proces634752977rocess @ A,Uv: proces634752977rocess @ A] : ( undefined @ ( proces634752977rocess @ A ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_67_process_Odisc__eq__case_I1_J,axiom,
% 3.59/1.85 ! [A: $tType] :
% 3.59/1.85 ( ( proces10484146Action @ A )
% 3.59/1.85 = ( proces1406508781rocess @ A @ $o
% 3.59/1.85 @ ^ [Uu: A,Uv2: proces634752977rocess @ A] : $true
% 3.59/1.85 @ ^ [Uu: proces634752977rocess @ A,Uv2: proces634752977rocess @ A] : $false ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_68_isAction__def,axiom,
% 3.59/1.85 ! [A: $tType] :
% 3.59/1.85 ( ( proces10484146Action @ A )
% 3.59/1.85 = ( ^ [Process2: proces634752977rocess @ A] :
% 3.59/1.85 ? [X112: A,X123: proces634752977rocess @ A] :
% 3.59/1.85 ( Process2
% 3.59/1.85 = ( proces1525233512Action @ A @ X112 @ X123 ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_69_process_OdiscI_I1_J,axiom,
% 3.59/1.85 ! [A: $tType,Process: proces634752977rocess @ A,X11: A,X122: proces634752977rocess @ A] :
% 3.59/1.85 ( ( Process
% 3.59/1.85 = ( proces1525233512Action @ A @ X11 @ X122 ) )
% 3.59/1.85 => ( proces10484146Action @ A @ Process ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_70_process_Odisc_I1_J,axiom,
% 3.59/1.85 ! [A: $tType,X11: A,X122: proces634752977rocess @ A] : ( proces10484146Action @ A @ ( proces1525233512Action @ A @ X11 @ X122 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_71_process_Osel_I2_J,axiom,
% 3.59/1.85 ! [A: $tType,X11: A,X122: proces634752977rocess @ A] :
% 3.59/1.85 ( ( proces1778668539contOf @ A @ ( proces1525233512Action @ A @ X11 @ X122 ) )
% 3.59/1.85 = X122 ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_72_CONT_Osimps_I1_J,axiom,
% 3.59/1.85 ! [B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X3: A] :
% 3.59/1.85 ( ( proces126235999e_CONT @ A @ B @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X3 ) )
% 3.59/1.85 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 3.59/1.85 @ ^ [Aa3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.59/1.85 @ ^ [P5: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P5 ) )
% 3.59/1.85 @ ^ [A5: B,T4: proces554692349s_term @ B @ A] : T4
% 3.59/1.85 @ ^ [Aa3: proces554692349s_term @ B @ A,Ab: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.59/1.85 @ ( Sys @ X3 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_73_isACT_Osimps_I2_J,axiom,
% 3.59/1.85 ! [A: $tType,C: $tType,B: $tType,D: $tType,Sys: A > ( proces554692349s_term @ B @ C ),P: proces634752977rocess @ D] :
% 3.59/1.85 ( ( proces687458811_isACT @ A @ B @ C @ D @ Sys @ ( proces1062592052s_PROC @ D @ A @ P ) )
% 3.59/1.85 = ( proces10484146Action @ D @ P ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_74_solution_Odisc_I1_J,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 3.59/1.85 => ( proces10484146Action @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_75_isACT_Osimps_I1_J,axiom,
% 3.59/1.85 ! [D: $tType,B: $tType,C: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ C ),X3: A] :
% 3.59/1.85 ( ( proces687458811_isACT @ A @ B @ C @ D @ Sys @ ( proces1627516585ss_VAR @ A @ D @ X3 ) )
% 3.59/1.85 = ( proces460752237s_term @ C @ $o @ B
% 3.59/1.85 @ ^ [Pvar2: C] : $false
% 3.59/1.85 @ ( proces10484146Action @ B )
% 3.59/1.85 @ ^ [A5: B,T4: proces554692349s_term @ B @ C] : $true
% 3.59/1.85 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 3.59/1.85 @ ( Sys @ X3 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_76_CONT_Osimps_I2_J,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),P: proces634752977rocess @ B] :
% 3.59/1.85 ( ( proces126235999e_CONT @ A @ B @ Sys @ ( proces1062592052s_PROC @ B @ A @ P ) )
% 3.59/1.85 = ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_77_prefOf__def,axiom,
% 3.59/1.85 ! [A: $tType] :
% 3.59/1.85 ( ( proces745025900prefOf @ A )
% 3.59/1.85 = ( proces1406508781rocess @ A @ A
% 3.59/1.85 @ ^ [X112: A,X123: proces634752977rocess @ A] : X112
% 3.59/1.85 @ ^ [Uu2: proces634752977rocess @ A,Uv: proces634752977rocess @ A] : ( undefined @ A ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_78_CONT_Oelims,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y3: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( ( ( proces126235999e_CONT @ A @ B @ X7 @ Xa )
% 3.59/1.85 = Y3 )
% 3.59/1.85 => ( ! [X4: A] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 3.59/1.85 => ( Y3
% 3.59/1.85 != ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 3.59/1.85 @ ^ [Aa3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.59/1.85 @ ^ [P5: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P5 ) )
% 3.59/1.85 @ ^ [A5: B,T4: proces554692349s_term @ B @ A] : T4
% 3.59/1.85 @ ^ [Aa3: proces554692349s_term @ B @ A,Ab: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.59/1.85 @ ( X7 @ X4 ) ) ) )
% 3.59/1.85 => ( ! [P4: proces634752977rocess @ B] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 3.59/1.85 => ( Y3
% 3.59/1.85 != ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P4 ) ) ) )
% 3.59/1.85 => ( ! [A3: B,T3: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) )
% 3.59/1.85 => ( Y3 != T3 ) )
% 3.59/1.85 => ~ ( ? [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( Xa
% 3.59/1.85 = ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 3.59/1.85 => ( Y3
% 3.59/1.85 != ( undefined @ ( proces554692349s_term @ B @ A ) ) ) ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_79_old_Oprod_Oinject,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,A2: A,B2: B,A6: A,B3: B] :
% 3.59/1.85 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 3.59/1.85 = ( product_Pair @ A @ B @ A6 @ B3 ) )
% 3.59/1.85 = ( ( A2 = A6 )
% 3.59/1.85 & ( B2 = B3 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_80_prod_Oinject,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,X1: A,X2: B,Y1: A,Y2: B] :
% 3.59/1.85 ( ( ( product_Pair @ A @ B @ X1 @ X2 )
% 3.59/1.85 = ( product_Pair @ A @ B @ Y1 @ Y2 ) )
% 3.59/1.85 = ( ( X1 = Y1 )
% 3.59/1.85 & ( X2 = Y2 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_81_PREF_Opelims,axiom,
% 3.59/1.85 ! [C: $tType,A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ B @ A,Y3: B] :
% 3.59/1.85 ( ( ( proces1708129104e_PREF @ A @ B @ C @ X7 @ Xa )
% 3.59/1.85 = Y3 )
% 3.59/1.85 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces527360425EF_rel @ A @ B @ C ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ Xa ) )
% 3.59/1.85 => ( ! [X4: A] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 3.59/1.85 => ( ( Y3
% 3.59/1.85 = ( proces460752237s_term @ C @ B @ B
% 3.59/1.85 @ ^ [Aa3: C] : ( undefined @ B )
% 3.59/1.85 @ ( proces745025900prefOf @ B )
% 3.59/1.85 @ ^ [A5: B,T4: proces554692349s_term @ B @ C] : A5
% 3.59/1.85 @ ^ [Aa3: proces554692349s_term @ B @ C,Ab: proces554692349s_term @ B @ C] : ( undefined @ B )
% 3.59/1.85 @ ( X7 @ X4 ) ) )
% 3.59/1.85 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces527360425EF_rel @ A @ B @ C ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) ) ) ) )
% 3.59/1.85 => ( ! [P4: proces634752977rocess @ B] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 3.59/1.85 => ( ( Y3
% 3.59/1.85 = ( proces745025900prefOf @ B @ P4 ) )
% 3.59/1.85 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces527360425EF_rel @ A @ B @ C ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) ) ) )
% 3.59/1.85 => ( ! [A3: B,T3: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) )
% 3.59/1.85 => ( ( Y3 = A3 )
% 3.59/1.85 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces527360425EF_rel @ A @ B @ C ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) ) ) ) )
% 3.59/1.85 => ~ ! [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 3.59/1.85 => ( ( Y3
% 3.59/1.85 = ( undefined @ B ) )
% 3.59/1.85 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces527360425EF_rel @ A @ B @ C ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_82_CONT_Opelims,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y3: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( ( ( proces126235999e_CONT @ A @ B @ X7 @ Xa )
% 3.59/1.85 = Y3 )
% 3.59/1.85 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1004198490NT_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ Xa ) )
% 3.59/1.85 => ( ! [X4: A] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 3.59/1.85 => ( ( Y3
% 3.59/1.85 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 3.59/1.85 @ ^ [Aa3: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.59/1.85 @ ^ [P5: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P5 ) )
% 3.59/1.85 @ ^ [A5: B,T4: proces554692349s_term @ B @ A] : T4
% 3.59/1.85 @ ^ [Aa3: proces554692349s_term @ B @ A,Ab: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.59/1.85 @ ( X7 @ X4 ) ) )
% 3.59/1.85 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1004198490NT_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) ) ) ) )
% 3.59/1.85 => ( ! [P4: proces634752977rocess @ B] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 3.59/1.85 => ( ( Y3
% 3.59/1.85 = ( proces1062592052s_PROC @ B @ A @ ( proces1778668539contOf @ B @ P4 ) ) )
% 3.59/1.85 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1004198490NT_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) ) ) )
% 3.59/1.85 => ( ! [A3: B,T3: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) )
% 3.59/1.85 => ( ( Y3 = T3 )
% 3.59/1.85 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1004198490NT_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1454156180ss_ACT @ B @ A @ A3 @ T3 ) ) ) ) )
% 3.59/1.85 => ~ ! [V: proces554692349s_term @ B @ A,Va: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces89589571ess_CH @ B @ A @ V @ Va ) )
% 3.59/1.85 => ( ( Y3
% 3.59/1.85 = ( undefined @ ( proces554692349s_term @ B @ A ) ) )
% 3.59/1.85 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1004198490NT_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces89589571ess_CH @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_83_isACT_Opelims_I1_J,axiom,
% 3.59/1.85 ! [B: $tType,C: $tType,A: $tType,D: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A,Y3: $o] :
% 3.59/1.85 ( ( ( proces687458811_isACT @ A @ B @ C @ D @ X7 @ Xa )
% 3.59/1.85 = Y3 )
% 3.59/1.85 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ Xa ) )
% 3.59/1.85 => ( ! [X4: A] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces1627516585ss_VAR @ A @ D @ X4 ) )
% 3.59/1.85 => ( ( Y3
% 3.59/1.85 = ( proces460752237s_term @ C @ $o @ B
% 3.59/1.85 @ ^ [Pvar2: C] : $false
% 3.59/1.85 @ ( proces10484146Action @ B )
% 3.59/1.85 @ ^ [A5: B,T4: proces554692349s_term @ B @ C] : $true
% 3.59/1.85 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 3.59/1.85 @ ( X7 @ X4 ) ) )
% 3.59/1.85 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ ( proces1627516585ss_VAR @ A @ D @ X4 ) ) ) ) )
% 3.59/1.85 => ( ! [P4: proces634752977rocess @ D] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 3.59/1.85 => ( ( Y3
% 3.59/1.85 = ( proces10484146Action @ D @ P4 ) )
% 3.59/1.85 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ ( proces1062592052s_PROC @ D @ A @ P4 ) ) ) ) )
% 3.59/1.85 => ( ! [A3: D,T3: proces554692349s_term @ D @ A] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces1454156180ss_ACT @ D @ A @ A3 @ T3 ) )
% 3.59/1.85 => ( Y3
% 3.59/1.85 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ ( proces1454156180ss_ACT @ D @ A @ A3 @ T3 ) ) ) ) )
% 3.59/1.85 => ~ ! [T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) )
% 3.59/1.85 => ( ~ Y3
% 3.59/1.85 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) ) ) ) ) ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_84_isACT_Opelims_I2_J,axiom,
% 3.59/1.85 ! [B: $tType,C: $tType,A: $tType,D: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A] :
% 3.59/1.85 ( ( proces687458811_isACT @ A @ B @ C @ D @ X7 @ Xa )
% 3.59/1.85 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ Xa ) )
% 3.59/1.85 => ( ! [X4: A] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces1627516585ss_VAR @ A @ D @ X4 ) )
% 3.59/1.85 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ ( proces1627516585ss_VAR @ A @ D @ X4 ) ) )
% 3.59/1.85 => ~ ( proces460752237s_term @ C @ $o @ B
% 3.59/1.85 @ ^ [Pvar2: C] : $false
% 3.59/1.85 @ ( proces10484146Action @ B )
% 3.59/1.85 @ ^ [A5: B,T4: proces554692349s_term @ B @ C] : $true
% 3.59/1.85 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 3.59/1.85 @ ( X7 @ X4 ) ) ) )
% 3.59/1.85 => ( ! [P4: proces634752977rocess @ D] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 3.59/1.85 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ ( proces1062592052s_PROC @ D @ A @ P4 ) ) )
% 3.59/1.85 => ~ ( proces10484146Action @ D @ P4 ) ) )
% 3.59/1.85 => ~ ! [A3: D,T3: proces554692349s_term @ D @ A] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces1454156180ss_ACT @ D @ A @ A3 @ T3 ) )
% 3.59/1.85 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ ( proces1454156180ss_ACT @ D @ A @ A3 @ T3 ) ) ) ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_85_isACT_Opelims_I3_J,axiom,
% 3.59/1.85 ! [B: $tType,C: $tType,A: $tType,D: $tType,X7: A > ( proces554692349s_term @ B @ C ),Xa: proces554692349s_term @ D @ A] :
% 3.59/1.85 ( ~ ( proces687458811_isACT @ A @ B @ C @ D @ X7 @ Xa )
% 3.59/1.85 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ Xa ) )
% 3.59/1.85 => ( ! [X4: A] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces1627516585ss_VAR @ A @ D @ X4 ) )
% 3.59/1.85 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ ( proces1627516585ss_VAR @ A @ D @ X4 ) ) )
% 3.59/1.85 => ( proces460752237s_term @ C @ $o @ B
% 3.59/1.85 @ ^ [Pvar2: C] : $false
% 3.59/1.85 @ ( proces10484146Action @ B )
% 3.59/1.85 @ ^ [A5: B,T4: proces554692349s_term @ B @ C] : $true
% 3.59/1.85 @ ^ [Process_term1: proces554692349s_term @ B @ C,Process_term2: proces554692349s_term @ B @ C] : $false
% 3.59/1.85 @ ( X7 @ X4 ) ) ) )
% 3.59/1.85 => ( ! [P4: proces634752977rocess @ D] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces1062592052s_PROC @ D @ A @ P4 ) )
% 3.59/1.85 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ ( proces1062592052s_PROC @ D @ A @ P4 ) ) )
% 3.59/1.85 => ( proces10484146Action @ D @ P4 ) ) )
% 3.59/1.85 => ~ ! [T12: proces554692349s_term @ D @ A,T23: proces554692349s_term @ D @ A] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) )
% 3.59/1.85 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) ) @ ( proces896239806CT_rel @ A @ B @ C @ D ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ C ) ) @ ( proces554692349s_term @ D @ A ) @ X7 @ ( proces89589571ess_CH @ D @ A @ T12 @ T23 ) ) ) ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_86_surj__pair,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,P: product_prod @ A @ B] :
% 3.59/1.85 ? [X6: A,Y4: B] :
% 3.59/1.85 ( P
% 3.59/1.85 = ( product_Pair @ A @ B @ X6 @ Y4 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_87_prod__cases,axiom,
% 3.59/1.85 ! [B: $tType,A: $tType,P3: ( product_prod @ A @ B ) > $o,P: product_prod @ A @ B] :
% 3.59/1.85 ( ! [A3: A,B4: B] : ( P3 @ ( product_Pair @ A @ B @ A3 @ B4 ) )
% 3.59/1.85 => ( P3 @ P ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_88_Pair__inject,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,A2: A,B2: B,A6: A,B3: B] :
% 3.59/1.85 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 3.59/1.85 = ( product_Pair @ A @ B @ A6 @ B3 ) )
% 3.59/1.85 => ~ ( ( A2 = A6 )
% 3.59/1.85 => ( B2 != B3 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_89_prod__cases3,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,C: $tType,Y3: product_prod @ A @ ( product_prod @ B @ C )] :
% 3.59/1.85 ~ ! [A3: A,B4: B,C2: C] :
% 3.59/1.85 ( Y3
% 3.59/1.85 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A3 @ ( product_Pair @ B @ C @ B4 @ C2 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_90_prod__cases4,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 3.59/1.85 ~ ! [A3: A,B4: B,C2: C,D2: D] :
% 3.59/1.85 ( Y3
% 3.59/1.85 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_91_prod__cases5,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,Y3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 3.59/1.85 ~ ! [A3: A,B4: B,C2: C,D2: D,E2: E] :
% 3.59/1.85 ( Y3
% 3.59/1.85 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C2 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_92_prod__cases6,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F5: $tType,Y3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) )] :
% 3.59/1.85 ~ ! [A3: A,B4: B,C2: C,D2: D,E2: E,F6: F5] :
% 3.59/1.85 ( Y3
% 3.59/1.85 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ F5 ) @ D2 @ ( product_Pair @ E @ F5 @ E2 @ F6 ) ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_93_prod__cases7,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F5: $tType,G2: $tType,Y3: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) ) )] :
% 3.59/1.85 ~ ! [A3: A,B4: B,C2: C,D2: D,E2: E,F6: F5,G3: G2] :
% 3.59/1.85 ( Y3
% 3.59/1.85 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F5 @ G2 ) @ E2 @ ( product_Pair @ F5 @ G2 @ F6 @ G3 ) ) ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_94_prod__induct3,axiom,
% 3.59/1.85 ! [C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X7: product_prod @ A @ ( product_prod @ B @ C )] :
% 3.59/1.85 ( ! [A3: A,B4: B,C2: C] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A3 @ ( product_Pair @ B @ C @ B4 @ C2 ) ) )
% 3.59/1.85 => ( P3 @ X7 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_95_prod__induct4,axiom,
% 3.59/1.85 ! [D: $tType,C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X7: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 3.59/1.85 ( ! [A3: A,B4: B,C2: C,D2: D] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) )
% 3.59/1.85 => ( P3 @ X7 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_96_prod__induct5,axiom,
% 3.59/1.85 ! [E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) > $o,X7: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 3.59/1.85 ( ! [A3: A,B4: B,C2: C,D2: D,E2: E] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C2 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) )
% 3.59/1.85 => ( P3 @ X7 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_97_prod__induct6,axiom,
% 3.59/1.85 ! [F5: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) ) ) > $o,X7: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) )] :
% 3.59/1.85 ( ! [A3: A,B4: B,C2: C,D2: D,E2: E,F6: F5] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F5 ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ F5 ) @ D2 @ ( product_Pair @ E @ F5 @ E2 @ F6 ) ) ) ) ) )
% 3.59/1.85 => ( P3 @ X7 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_98_prod__induct7,axiom,
% 3.59/1.85 ! [G2: $tType,F5: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P3: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) ) ) ) > $o,X7: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) ) )] :
% 3.59/1.85 ( ! [A3: A,B4: B,C2: C,D2: D,E2: E,F6: F5,G3: G2] : ( P3 @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F5 @ G2 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F5 @ G2 ) @ E2 @ ( product_Pair @ F5 @ G2 @ F6 @ G3 ) ) ) ) ) ) )
% 3.59/1.85 => ( P3 @ X7 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_99_old_Oprod_Oexhaust,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,Y3: product_prod @ A @ B] :
% 3.59/1.85 ~ ! [A3: A,B4: B] :
% 3.59/1.85 ( Y3
% 3.59/1.85 != ( product_Pair @ A @ B @ A3 @ B4 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_100_old_Oprod_Oinducts,axiom,
% 3.59/1.85 ! [B: $tType,A: $tType,P3: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 3.59/1.85 ( ! [A3: A,B4: B] : ( P3 @ ( product_Pair @ A @ B @ A3 @ B4 ) )
% 3.59/1.85 => ( P3 @ Prod ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_101_old_Oprod_Orec,axiom,
% 3.59/1.85 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 3.59/1.85 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 3.59/1.85 = ( F1 @ A2 @ B2 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_102_CH1_Oelims,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y3: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( ( ( proces1239275103le_CH1 @ A @ B @ X7 @ Xa )
% 3.59/1.85 = Y3 )
% 3.59/1.85 => ( ! [X4: A] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 3.59/1.85 => ( Y3
% 3.59/1.85 != ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 3.59/1.85 @ ^ [A5: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.59/1.85 @ ^ [P5: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P5 ) )
% 3.59/1.85 @ ^ [A5: B,B5: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.59/1.85 @ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T13
% 3.59/1.85 @ ( X7 @ X4 ) ) ) )
% 3.59/1.85 => ( ! [P4: proces634752977rocess @ B] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 3.59/1.85 => ( Y3
% 3.59/1.85 != ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P4 ) ) ) )
% 3.59/1.85 => ( ! [T12: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( ? [T23: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( Xa
% 3.59/1.85 = ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
% 3.59/1.85 => ( Y3 != T12 ) )
% 3.59/1.85 => ~ ( ? [V: B,Va: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( Xa
% 3.59/1.85 = ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
% 3.59/1.85 => ( Y3
% 3.59/1.85 != ( undefined @ ( proces554692349s_term @ B @ A ) ) ) ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_103_CH2_Oelims,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y3: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( ( ( proces1239275104le_CH2 @ A @ B @ X7 @ Xa )
% 3.59/1.85 = Y3 )
% 3.59/1.85 => ( ! [X4: A] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 3.59/1.85 => ( Y3
% 3.59/1.85 != ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 3.59/1.85 @ ^ [A5: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.59/1.85 @ ^ [P5: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P5 ) )
% 3.59/1.85 @ ^ [A5: B,B5: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.59/1.85 @ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T24
% 3.59/1.85 @ ( X7 @ X4 ) ) ) )
% 3.59/1.85 => ( ! [P4: proces634752977rocess @ B] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 3.59/1.85 => ( Y3
% 3.59/1.85 != ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P4 ) ) ) )
% 3.59/1.85 => ( ! [T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
% 3.59/1.85 => ( Y3 != T23 ) )
% 3.59/1.85 => ~ ( ? [V: B,Va: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( Xa
% 3.59/1.85 = ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
% 3.59/1.85 => ( Y3
% 3.59/1.85 != ( undefined @ ( proces554692349s_term @ B @ A ) ) ) ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_104_CH1_Opelims,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y3: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( ( ( proces1239275103le_CH1 @ A @ B @ X7 @ Xa )
% 3.59/1.85 = Y3 )
% 3.59/1.85 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1869379930H1_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ Xa ) )
% 3.59/1.85 => ( ! [X4: A] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 3.59/1.85 => ( ( Y3
% 3.59/1.85 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 3.59/1.85 @ ^ [A5: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.59/1.85 @ ^ [P5: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P5 ) )
% 3.59/1.85 @ ^ [A5: B,B5: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.59/1.85 @ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T13
% 3.59/1.85 @ ( X7 @ X4 ) ) )
% 3.59/1.85 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1869379930H1_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) ) ) ) )
% 3.59/1.85 => ( ! [P4: proces634752977rocess @ B] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 3.59/1.85 => ( ( Y3
% 3.59/1.85 = ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P4 ) ) )
% 3.59/1.85 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1869379930H1_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) ) ) )
% 3.59/1.85 => ( ! [T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
% 3.59/1.85 => ( ( Y3 = T12 )
% 3.59/1.85 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1869379930H1_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) ) ) ) )
% 3.59/1.85 => ~ ! [V: B,Va: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
% 3.59/1.85 => ( ( Y3
% 3.59/1.85 = ( undefined @ ( proces554692349s_term @ B @ A ) ) )
% 3.59/1.85 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces1869379930H1_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_105_CH2_Opelims,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,X7: A > ( proces554692349s_term @ B @ A ),Xa: proces554692349s_term @ B @ A,Y3: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( ( ( proces1239275104le_CH2 @ A @ B @ X7 @ Xa )
% 3.59/1.85 = Y3 )
% 3.59/1.85 => ( ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces93903513H2_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ Xa ) )
% 3.59/1.85 => ( ! [X4: A] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces1627516585ss_VAR @ A @ B @ X4 ) )
% 3.59/1.85 => ( ( Y3
% 3.59/1.85 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 3.59/1.85 @ ^ [A5: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.59/1.85 @ ^ [P5: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P5 ) )
% 3.59/1.85 @ ^ [A5: B,B5: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.59/1.85 @ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T24
% 3.59/1.85 @ ( X7 @ X4 ) ) )
% 3.59/1.85 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces93903513H2_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1627516585ss_VAR @ A @ B @ X4 ) ) ) ) )
% 3.59/1.85 => ( ! [P4: proces634752977rocess @ B] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces1062592052s_PROC @ B @ A @ P4 ) )
% 3.59/1.85 => ( ( Y3
% 3.59/1.85 = ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P4 ) ) )
% 3.59/1.85 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces93903513H2_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1062592052s_PROC @ B @ A @ P4 ) ) ) ) )
% 3.59/1.85 => ( ! [T12: proces554692349s_term @ B @ A,T23: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) )
% 3.59/1.85 => ( ( Y3 = T23 )
% 3.59/1.85 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces93903513H2_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces89589571ess_CH @ B @ A @ T12 @ T23 ) ) ) ) )
% 3.59/1.85 => ~ ! [V: B,Va: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( ( Xa
% 3.59/1.85 = ( proces1454156180ss_ACT @ B @ A @ V @ Va ) )
% 3.59/1.85 => ( ( Y3
% 3.59/1.85 = ( undefined @ ( proces554692349s_term @ B @ A ) ) )
% 3.59/1.85 => ~ ( accp @ ( product_prod @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) ) @ ( proces93903513H2_rel @ A @ B ) @ ( product_Pair @ ( A > ( proces554692349s_term @ B @ A ) ) @ ( proces554692349s_term @ B @ A ) @ X7 @ ( proces1454156180ss_ACT @ B @ A @ V @ Va ) ) ) ) ) ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_106_ch1Of__def,axiom,
% 3.59/1.85 ! [A: $tType] :
% 3.59/1.85 ( ( proces979765041_ch1Of @ A )
% 3.59/1.85 = ( proces1406508781rocess @ A @ ( proces634752977rocess @ A )
% 3.59/1.85 @ ^ [Uu2: A,Uv: proces634752977rocess @ A] : ( undefined @ ( proces634752977rocess @ A ) )
% 3.59/1.85 @ ^ [X21: proces634752977rocess @ A,X222: proces634752977rocess @ A] : X21 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_107_CH2_Osimps_I2_J,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),P: proces634752977rocess @ B] :
% 3.59/1.85 ( ( proces1239275104le_CH2 @ A @ B @ Sys @ ( proces1062592052s_PROC @ B @ A @ P ) )
% 3.59/1.85 = ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_108_CH1_Osimps_I2_J,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),P: proces634752977rocess @ B] :
% 3.59/1.85 ( ( proces1239275103le_CH1 @ A @ B @ Sys @ ( proces1062592052s_PROC @ B @ A @ P ) )
% 3.59/1.85 = ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_109_solution_Osimps_I6_J,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 3.59/1.85 => ( ( proces988026546_ch2Of @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 3.59/1.85 = ( proces1652378886lution @ A @ B @ Sys @ ( proces1239275104le_CH2 @ A @ B @ Sys @ T2 ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_110_solution_Osimps_I5_J,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 3.59/1.85 => ( ( proces979765041_ch1Of @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 3.59/1.85 = ( proces1652378886lution @ A @ B @ Sys @ ( proces1239275103le_CH1 @ A @ B @ Sys @ T2 ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_111_CH2_Osimps_I3_J,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T1: proces554692349s_term @ B @ A,T22: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( ( proces1239275104le_CH2 @ A @ B @ Sys @ ( proces89589571ess_CH @ B @ A @ T1 @ T22 ) )
% 3.59/1.85 = T22 ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_112_CH1_Osimps_I3_J,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T1: proces554692349s_term @ B @ A,T22: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( ( proces1239275103le_CH1 @ A @ B @ Sys @ ( proces89589571ess_CH @ B @ A @ T1 @ T22 ) )
% 3.59/1.85 = T1 ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_113_process_Ocase__eq__if,axiom,
% 3.59/1.85 ! [B: $tType,A: $tType] :
% 3.59/1.85 ( ( proces1406508781rocess @ A @ B )
% 3.59/1.85 = ( ^ [F12: A > ( proces634752977rocess @ A ) > B,F22: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process2: proces634752977rocess @ A] : ( if @ B @ ( proces10484146Action @ A @ Process2 ) @ ( F12 @ ( proces745025900prefOf @ A @ Process2 ) @ ( proces1778668539contOf @ A @ Process2 ) ) @ ( F22 @ ( proces979765041_ch1Of @ A @ Process2 ) @ ( proces988026546_ch2Of @ A @ Process2 ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_114_CH2_Osimps_I1_J,axiom,
% 3.59/1.85 ! [B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X3: A] :
% 3.59/1.85 ( ( proces1239275104le_CH2 @ A @ B @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X3 ) )
% 3.59/1.85 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 3.59/1.85 @ ^ [A5: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.59/1.85 @ ^ [P5: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces988026546_ch2Of @ B @ P5 ) )
% 3.59/1.85 @ ^ [A5: B,B5: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.59/1.85 @ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T24
% 3.59/1.85 @ ( Sys @ X3 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_115_CH1_Osimps_I1_J,axiom,
% 3.59/1.85 ! [B: $tType,A: $tType,Sys: A > ( proces554692349s_term @ B @ A ),X3: A] :
% 3.59/1.85 ( ( proces1239275103le_CH1 @ A @ B @ Sys @ ( proces1627516585ss_VAR @ A @ B @ X3 ) )
% 3.59/1.85 = ( proces460752237s_term @ A @ ( proces554692349s_term @ B @ A ) @ B
% 3.59/1.85 @ ^ [A5: A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.59/1.85 @ ^ [P5: proces634752977rocess @ B] : ( proces1062592052s_PROC @ B @ A @ ( proces979765041_ch1Of @ B @ P5 ) )
% 3.59/1.85 @ ^ [A5: B,B5: proces554692349s_term @ B @ A] : ( undefined @ ( proces554692349s_term @ B @ A ) )
% 3.59/1.85 @ ^ [T13: proces554692349s_term @ B @ A,T24: proces554692349s_term @ B @ A] : T13
% 3.59/1.85 @ ( Sys @ X3 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_116_ch2Of__def,axiom,
% 3.59/1.85 ! [A: $tType] :
% 3.59/1.85 ( ( proces988026546_ch2Of @ A )
% 3.59/1.85 = ( proces1406508781rocess @ A @ ( proces634752977rocess @ A )
% 3.59/1.85 @ ^ [Uu2: A,Uv: proces634752977rocess @ A] : ( undefined @ ( proces634752977rocess @ A ) )
% 3.59/1.85 @ ^ [X21: proces634752977rocess @ A,X222: proces634752977rocess @ A] : X222 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_117_solution_Ocode,axiom,
% 3.59/1.85 ! [B: $tType,A: $tType] :
% 3.59/1.85 ( ( proces1652378886lution @ A @ B )
% 3.59/1.85 = ( ^ [Sys3: A > ( proces554692349s_term @ B @ A ),T4: proces554692349s_term @ B @ A] : ( if @ ( proces634752977rocess @ B ) @ ( proces687458811_isACT @ A @ B @ A @ B @ Sys3 @ T4 ) @ ( proces1525233512Action @ B @ ( proces1708129104e_PREF @ A @ B @ A @ Sys3 @ T4 ) @ ( proces1652378886lution @ A @ B @ Sys3 @ ( proces126235999e_CONT @ A @ B @ Sys3 @ T4 ) ) ) @ ( proces1915862579Choice @ B @ ( proces1652378886lution @ A @ B @ Sys3 @ ( proces1239275103le_CH1 @ A @ B @ Sys3 @ T4 ) ) @ ( proces1652378886lution @ A @ B @ Sys3 @ ( proces1239275104le_CH2 @ A @ B @ Sys3 @ T4 ) ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_118_process_Osplit__sel__asm,axiom,
% 3.59/1.85 ! [B: $tType,A: $tType,P3: B > $o,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process: proces634752977rocess @ A] :
% 3.59/1.85 ( ( P3 @ ( proces1406508781rocess @ A @ B @ F1 @ F2 @ Process ) )
% 3.59/1.85 = ( ~ ( ( ( Process
% 3.59/1.85 = ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) )
% 3.59/1.85 & ~ ( P3 @ ( F1 @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) ) )
% 3.59/1.85 | ( ( Process
% 3.59/1.85 = ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) )
% 3.59/1.85 & ~ ( P3 @ ( F2 @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_119_process_Osplit__sel,axiom,
% 3.59/1.85 ! [B: $tType,A: $tType,P3: B > $o,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,Process: proces634752977rocess @ A] :
% 3.59/1.85 ( ( P3 @ ( proces1406508781rocess @ A @ B @ F1 @ F2 @ Process ) )
% 3.59/1.85 = ( ( ( Process
% 3.59/1.85 = ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) )
% 3.59/1.85 => ( P3 @ ( F1 @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) ) )
% 3.59/1.85 & ( ( Process
% 3.59/1.85 = ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) )
% 3.59/1.85 => ( P3 @ ( F2 @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_120_process_Oexpand,axiom,
% 3.59/1.85 ! [A: $tType,Process: proces634752977rocess @ A,Process3: proces634752977rocess @ A] :
% 3.59/1.85 ( ( ( proces10484146Action @ A @ Process )
% 3.59/1.85 = ( proces10484146Action @ A @ Process3 ) )
% 3.59/1.85 => ( ( ( proces10484146Action @ A @ Process )
% 3.59/1.85 => ( ( proces10484146Action @ A @ Process3 )
% 3.59/1.85 => ( ( ( proces745025900prefOf @ A @ Process )
% 3.59/1.85 = ( proces745025900prefOf @ A @ Process3 ) )
% 3.59/1.85 & ( ( proces1778668539contOf @ A @ Process )
% 3.59/1.85 = ( proces1778668539contOf @ A @ Process3 ) ) ) ) )
% 3.59/1.85 => ( ( ( proces401113213Choice @ A @ Process )
% 3.59/1.85 => ( ( proces401113213Choice @ A @ Process3 )
% 3.59/1.85 => ( ( ( proces979765041_ch1Of @ A @ Process )
% 3.59/1.85 = ( proces979765041_ch1Of @ A @ Process3 ) )
% 3.59/1.85 & ( ( proces988026546_ch2Of @ A @ Process )
% 3.59/1.85 = ( proces988026546_ch2Of @ A @ Process3 ) ) ) ) )
% 3.59/1.85 => ( Process = Process3 ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_121_process_Ocoinduct,axiom,
% 3.59/1.85 ! [A: $tType,R: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,Process: proces634752977rocess @ A,Process3: proces634752977rocess @ A] :
% 3.59/1.85 ( ( R @ Process @ Process3 )
% 3.59/1.85 => ( ! [Process4: proces634752977rocess @ A,Process5: proces634752977rocess @ A] :
% 3.59/1.85 ( ( R @ Process4 @ Process5 )
% 3.59/1.85 => ( ( ( proces10484146Action @ A @ Process4 )
% 3.59/1.85 = ( proces10484146Action @ A @ Process5 ) )
% 3.59/1.85 & ( ( proces10484146Action @ A @ Process4 )
% 3.59/1.85 => ( ( proces10484146Action @ A @ Process5 )
% 3.59/1.85 => ( ( ( proces745025900prefOf @ A @ Process4 )
% 3.59/1.85 = ( proces745025900prefOf @ A @ Process5 ) )
% 3.59/1.85 & ( R @ ( proces1778668539contOf @ A @ Process4 ) @ ( proces1778668539contOf @ A @ Process5 ) ) ) ) )
% 3.59/1.85 & ( ( proces401113213Choice @ A @ Process4 )
% 3.59/1.85 => ( ( proces401113213Choice @ A @ Process5 )
% 3.59/1.85 => ( ( R @ ( proces979765041_ch1Of @ A @ Process4 ) @ ( proces979765041_ch1Of @ A @ Process5 ) )
% 3.59/1.85 & ( R @ ( proces988026546_ch2Of @ A @ Process4 ) @ ( proces988026546_ch2Of @ A @ Process5 ) ) ) ) ) ) )
% 3.59/1.85 => ( Process = Process3 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_122_process_Oinject_I2_J,axiom,
% 3.59/1.85 ! [A: $tType,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A,Y21: proces634752977rocess @ A,Y22: proces634752977rocess @ A] :
% 3.59/1.85 ( ( ( proces1915862579Choice @ A @ X212 @ X223 )
% 3.59/1.85 = ( proces1915862579Choice @ A @ Y21 @ Y22 ) )
% 3.59/1.85 = ( ( X212 = Y21 )
% 3.59/1.85 & ( X223 = Y22 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_123_process_Opred__inject_I2_J,axiom,
% 3.59/1.85 ! [A: $tType,P3: A > $o,A2: proces634752977rocess @ A,Aa2: proces634752977rocess @ A] :
% 3.59/1.85 ( ( proces1205983068rocess @ A @ P3 @ ( proces1915862579Choice @ A @ A2 @ Aa2 ) )
% 3.59/1.85 = ( ( proces1205983068rocess @ A @ P3 @ A2 )
% 3.59/1.85 & ( proces1205983068rocess @ A @ P3 @ Aa2 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_124_solution_Odisc__iff_I2_J,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( ( proces401113213Choice @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) )
% 3.59/1.85 = ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_125_process_Ocollapse_I2_J,axiom,
% 3.59/1.85 ! [A: $tType,Process: proces634752977rocess @ A] :
% 3.59/1.85 ( ( proces401113213Choice @ A @ Process )
% 3.59/1.85 => ( ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) )
% 3.59/1.85 = Process ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_126_process_Odisc_I4_J,axiom,
% 3.59/1.85 ! [A: $tType,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A] : ( proces401113213Choice @ A @ ( proces1915862579Choice @ A @ X212 @ X223 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_127_process_OdiscI_I2_J,axiom,
% 3.59/1.85 ! [A: $tType,Process: proces634752977rocess @ A,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A] :
% 3.59/1.85 ( ( Process
% 3.59/1.85 = ( proces1915862579Choice @ A @ X212 @ X223 ) )
% 3.59/1.85 => ( proces401113213Choice @ A @ Process ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_128_isChoice__def,axiom,
% 3.59/1.85 ! [A: $tType] :
% 3.59/1.85 ( ( proces401113213Choice @ A )
% 3.59/1.85 = ( ^ [Process2: proces634752977rocess @ A] :
% 3.59/1.85 ? [X21: proces634752977rocess @ A,X222: proces634752977rocess @ A] :
% 3.59/1.85 ( Process2
% 3.59/1.85 = ( proces1915862579Choice @ A @ X21 @ X222 ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_129_process__strong__coind,axiom,
% 3.59/1.85 ! [A: $tType,Phi: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,P: proces634752977rocess @ A,P6: proces634752977rocess @ A] :
% 3.59/1.85 ( ( Phi @ P @ P6 )
% 3.59/1.85 => ( ! [P4: proces634752977rocess @ A,P7: proces634752977rocess @ A] :
% 3.59/1.85 ( ( Phi @ P4 @ P7 )
% 3.59/1.85 => ( ( ( proces10484146Action @ A @ P4 )
% 3.59/1.85 = ( proces10484146Action @ A @ P7 ) )
% 3.59/1.85 & ( ( proces401113213Choice @ A @ P4 )
% 3.59/1.85 = ( proces401113213Choice @ A @ P7 ) ) ) )
% 3.59/1.85 => ( ! [A3: A,A7: A,P4: proces634752977rocess @ A,P7: proces634752977rocess @ A] :
% 3.59/1.85 ( ( Phi @ ( proces1525233512Action @ A @ A3 @ P4 ) @ ( proces1525233512Action @ A @ A7 @ P7 ) )
% 3.59/1.85 => ( ( A3 = A7 )
% 3.59/1.85 & ( ( Phi @ P4 @ P7 )
% 3.59/1.85 | ( P4 = P7 ) ) ) )
% 3.59/1.85 => ( ! [P4: proces634752977rocess @ A,Q2: proces634752977rocess @ A,P7: proces634752977rocess @ A,Q3: proces634752977rocess @ A] :
% 3.59/1.85 ( ( Phi @ ( proces1915862579Choice @ A @ P4 @ Q2 ) @ ( proces1915862579Choice @ A @ P7 @ Q3 ) )
% 3.59/1.85 => ( ( ( Phi @ P4 @ P7 )
% 3.59/1.85 | ( P4 = P7 ) )
% 3.59/1.85 & ( ( Phi @ Q2 @ Q3 )
% 3.59/1.85 | ( Q2 = Q3 ) ) ) )
% 3.59/1.85 => ( P = P6 ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_130_process__coind,axiom,
% 3.59/1.85 ! [A: $tType,Phi: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,P: proces634752977rocess @ A,P6: proces634752977rocess @ A] :
% 3.59/1.85 ( ( Phi @ P @ P6 )
% 3.59/1.85 => ( ! [P4: proces634752977rocess @ A,P7: proces634752977rocess @ A] :
% 3.59/1.85 ( ( Phi @ P4 @ P7 )
% 3.59/1.85 => ( ( ( proces10484146Action @ A @ P4 )
% 3.59/1.85 = ( proces10484146Action @ A @ P7 ) )
% 3.59/1.85 & ( ( proces401113213Choice @ A @ P4 )
% 3.59/1.85 = ( proces401113213Choice @ A @ P7 ) ) ) )
% 3.59/1.85 => ( ! [A3: A,A7: A,P4: proces634752977rocess @ A,P7: proces634752977rocess @ A] :
% 3.59/1.85 ( ( Phi @ ( proces1525233512Action @ A @ A3 @ P4 ) @ ( proces1525233512Action @ A @ A7 @ P7 ) )
% 3.59/1.85 => ( ( A3 = A7 )
% 3.59/1.85 & ( Phi @ P4 @ P7 ) ) )
% 3.59/1.85 => ( ! [P4: proces634752977rocess @ A,Q2: proces634752977rocess @ A,P7: proces634752977rocess @ A,Q3: proces634752977rocess @ A] :
% 3.59/1.85 ( ( Phi @ ( proces1915862579Choice @ A @ P4 @ Q2 ) @ ( proces1915862579Choice @ A @ P7 @ Q3 ) )
% 3.59/1.85 => ( ( Phi @ P4 @ P7 )
% 3.59/1.85 & ( Phi @ Q2 @ Q3 ) ) )
% 3.59/1.85 => ( P = P6 ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_131_process_Odisc_I2_J,axiom,
% 3.59/1.85 ! [A: $tType,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A] :
% 3.59/1.85 ~ ( proces10484146Action @ A @ ( proces1915862579Choice @ A @ X212 @ X223 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_132_process_Odistinct_I1_J,axiom,
% 3.59/1.85 ! [A: $tType,X11: A,X122: proces634752977rocess @ A,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A] :
% 3.59/1.85 ( ( proces1525233512Action @ A @ X11 @ X122 )
% 3.59/1.85 != ( proces1915862579Choice @ A @ X212 @ X223 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_133_process_Oexhaust,axiom,
% 3.59/1.85 ! [A: $tType,Y3: proces634752977rocess @ A] :
% 3.59/1.85 ( ! [X113: A,X124: proces634752977rocess @ A] :
% 3.59/1.85 ( Y3
% 3.59/1.85 != ( proces1525233512Action @ A @ X113 @ X124 ) )
% 3.59/1.85 => ~ ! [X213: proces634752977rocess @ A,X224: proces634752977rocess @ A] :
% 3.59/1.85 ( Y3
% 3.59/1.85 != ( proces1915862579Choice @ A @ X213 @ X224 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_134_process_Osel_I4_J,axiom,
% 3.59/1.85 ! [A: $tType,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A] :
% 3.59/1.85 ( ( proces988026546_ch2Of @ A @ ( proces1915862579Choice @ A @ X212 @ X223 ) )
% 3.59/1.85 = X223 ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_135_process_Osel_I3_J,axiom,
% 3.59/1.85 ! [A: $tType,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A] :
% 3.59/1.85 ( ( proces979765041_ch1Of @ A @ ( proces1915862579Choice @ A @ X212 @ X223 ) )
% 3.59/1.85 = X212 ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_136_process_Odistinct__disc_I2_J,axiom,
% 3.59/1.85 ! [A: $tType,Process: proces634752977rocess @ A] :
% 3.59/1.85 ( ( proces401113213Choice @ A @ Process )
% 3.59/1.85 => ~ ( proces10484146Action @ A @ Process ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_137_process_Odistinct__disc_I1_J,axiom,
% 3.59/1.85 ! [A: $tType,Process: proces634752977rocess @ A] :
% 3.59/1.85 ( ( proces10484146Action @ A @ Process )
% 3.59/1.85 => ~ ( proces401113213Choice @ A @ Process ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_138_isAction__isChoice,axiom,
% 3.59/1.85 ! [A: $tType,P: proces634752977rocess @ A] :
% 3.59/1.85 ( ( proces10484146Action @ A @ P )
% 3.59/1.85 | ( proces401113213Choice @ A @ P ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_139_process_Oexhaust__disc,axiom,
% 3.59/1.85 ! [A: $tType,Process: proces634752977rocess @ A] :
% 3.59/1.85 ( ~ ( proces10484146Action @ A @ Process )
% 3.59/1.85 => ( proces401113213Choice @ A @ Process ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_140_not__isAction__isChoice,axiom,
% 3.59/1.85 ! [A: $tType,P: proces634752977rocess @ A] :
% 3.59/1.85 ~ ( ( proces10484146Action @ A @ P )
% 3.59/1.85 & ( proces401113213Choice @ A @ P ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_141_process_Odisc_I3_J,axiom,
% 3.59/1.85 ! [A: $tType,X11: A,X122: proces634752977rocess @ A] :
% 3.59/1.85 ~ ( proces401113213Choice @ A @ ( proces1525233512Action @ A @ X11 @ X122 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_142_process_Osimps_I6_J,axiom,
% 3.59/1.85 ! [B: $tType,A: $tType,F1: A > ( proces634752977rocess @ A ) > B,F2: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > B,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A] :
% 3.59/1.85 ( ( proces1406508781rocess @ A @ B @ F1 @ F2 @ ( proces1915862579Choice @ A @ X212 @ X223 ) )
% 3.59/1.85 = ( F2 @ X212 @ X223 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_143_solution_Odisc_I2_J,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 3.59/1.85 => ( proces401113213Choice @ B @ ( proces1652378886lution @ A @ B @ Sys @ T2 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_144_process_Odisc__eq__case_I2_J,axiom,
% 3.59/1.85 ! [A: $tType] :
% 3.59/1.85 ( ( proces401113213Choice @ A )
% 3.59/1.85 = ( proces1406508781rocess @ A @ $o
% 3.59/1.85 @ ^ [Uu: A,Uv2: proces634752977rocess @ A] : $false
% 3.59/1.85 @ ^ [Uu: proces634752977rocess @ A,Uv2: proces634752977rocess @ A] : $true ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_145_solution_Octr_I2_J,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,Sys: A > ( proces554692349s_term @ B @ A ),T2: proces554692349s_term @ B @ A] :
% 3.59/1.85 ( ~ ( proces687458811_isACT @ A @ B @ A @ B @ Sys @ T2 )
% 3.59/1.85 => ( ( proces1652378886lution @ A @ B @ Sys @ T2 )
% 3.59/1.85 = ( proces1915862579Choice @ B @ ( proces1652378886lution @ A @ B @ Sys @ ( proces1239275103le_CH1 @ A @ B @ Sys @ T2 ) ) @ ( proces1652378886lution @ A @ B @ Sys @ ( proces1239275104le_CH2 @ A @ B @ Sys @ T2 ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_146_process_Oexhaust__sel,axiom,
% 3.59/1.85 ! [A: $tType,Process: proces634752977rocess @ A] :
% 3.59/1.85 ( ( Process
% 3.59/1.85 != ( proces1525233512Action @ A @ ( proces745025900prefOf @ A @ Process ) @ ( proces1778668539contOf @ A @ Process ) ) )
% 3.59/1.85 => ( Process
% 3.59/1.85 = ( proces1915862579Choice @ A @ ( proces979765041_ch1Of @ A @ Process ) @ ( proces988026546_ch2Of @ A @ Process ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_147_process_Ocoinduct__strong,axiom,
% 3.59/1.85 ! [A: $tType,R: ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > $o,Process: proces634752977rocess @ A,Process3: proces634752977rocess @ A] :
% 3.59/1.85 ( ( R @ Process @ Process3 )
% 3.59/1.85 => ( ! [Process4: proces634752977rocess @ A,Process5: proces634752977rocess @ A] :
% 3.59/1.85 ( ( R @ Process4 @ Process5 )
% 3.59/1.85 => ( ( ( proces10484146Action @ A @ Process4 )
% 3.59/1.85 = ( proces10484146Action @ A @ Process5 ) )
% 3.59/1.85 & ( ( proces10484146Action @ A @ Process4 )
% 3.59/1.85 => ( ( proces10484146Action @ A @ Process5 )
% 3.59/1.85 => ( ( ( proces745025900prefOf @ A @ Process4 )
% 3.59/1.85 = ( proces745025900prefOf @ A @ Process5 ) )
% 3.59/1.85 & ( ( R @ ( proces1778668539contOf @ A @ Process4 ) @ ( proces1778668539contOf @ A @ Process5 ) )
% 3.59/1.85 | ( ( proces1778668539contOf @ A @ Process4 )
% 3.59/1.85 = ( proces1778668539contOf @ A @ Process5 ) ) ) ) ) )
% 3.59/1.85 & ( ( proces401113213Choice @ A @ Process4 )
% 3.59/1.85 => ( ( proces401113213Choice @ A @ Process5 )
% 3.59/1.85 => ( ( ( R @ ( proces979765041_ch1Of @ A @ Process4 ) @ ( proces979765041_ch1Of @ A @ Process5 ) )
% 3.59/1.85 | ( ( proces979765041_ch1Of @ A @ Process4 )
% 3.59/1.85 = ( proces979765041_ch1Of @ A @ Process5 ) ) )
% 3.59/1.85 & ( ( R @ ( proces988026546_ch2Of @ A @ Process4 ) @ ( proces988026546_ch2Of @ A @ Process5 ) )
% 3.59/1.85 | ( ( proces988026546_ch2Of @ A @ Process4 )
% 3.59/1.85 = ( proces988026546_ch2Of @ A @ Process5 ) ) ) ) ) ) ) )
% 3.59/1.85 => ( Process = Process3 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_148_process_Orel__sel,axiom,
% 3.59/1.85 ! [B: $tType,A: $tType] :
% 3.59/1.85 ( ( proces749077512rocess @ A @ B )
% 3.59/1.85 = ( ^ [R2: A > B > $o,A5: proces634752977rocess @ A,B5: proces634752977rocess @ B] :
% 3.59/1.85 ( ( ( proces10484146Action @ A @ A5 )
% 3.59/1.85 = ( proces10484146Action @ B @ B5 ) )
% 3.59/1.85 & ( ( proces10484146Action @ A @ A5 )
% 3.59/1.85 => ( ( proces10484146Action @ B @ B5 )
% 3.59/1.85 => ( ( R2 @ ( proces745025900prefOf @ A @ A5 ) @ ( proces745025900prefOf @ B @ B5 ) )
% 3.59/1.85 & ( proces749077512rocess @ A @ B @ R2 @ ( proces1778668539contOf @ A @ A5 ) @ ( proces1778668539contOf @ B @ B5 ) ) ) ) )
% 3.59/1.85 & ( ( proces401113213Choice @ A @ A5 )
% 3.59/1.85 => ( ( proces401113213Choice @ B @ B5 )
% 3.59/1.85 => ( ( proces749077512rocess @ A @ B @ R2 @ ( proces979765041_ch1Of @ A @ A5 ) @ ( proces979765041_ch1Of @ B @ B5 ) )
% 3.59/1.85 & ( proces749077512rocess @ A @ B @ R2 @ ( proces988026546_ch2Of @ A @ A5 ) @ ( proces988026546_ch2Of @ B @ B5 ) ) ) ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_149_process_Orel__coinduct,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,P3: ( proces634752977rocess @ A ) > ( proces634752977rocess @ B ) > $o,X7: proces634752977rocess @ A,Y3: proces634752977rocess @ B,R: A > B > $o] :
% 3.59/1.85 ( ( P3 @ X7 @ Y3 )
% 3.59/1.85 => ( ! [Process4: proces634752977rocess @ A,Process5: proces634752977rocess @ B] :
% 3.59/1.85 ( ( P3 @ Process4 @ Process5 )
% 3.59/1.85 => ( ( ( proces10484146Action @ A @ Process4 )
% 3.59/1.85 = ( proces10484146Action @ B @ Process5 ) )
% 3.59/1.85 & ( ( proces10484146Action @ A @ Process4 )
% 3.59/1.85 => ( ( proces10484146Action @ B @ Process5 )
% 3.59/1.85 => ( ( R @ ( proces745025900prefOf @ A @ Process4 ) @ ( proces745025900prefOf @ B @ Process5 ) )
% 3.59/1.85 & ( P3 @ ( proces1778668539contOf @ A @ Process4 ) @ ( proces1778668539contOf @ B @ Process5 ) ) ) ) )
% 3.59/1.85 & ( ( proces401113213Choice @ A @ Process4 )
% 3.59/1.85 => ( ( proces401113213Choice @ B @ Process5 )
% 3.59/1.85 => ( ( P3 @ ( proces979765041_ch1Of @ A @ Process4 ) @ ( proces979765041_ch1Of @ B @ Process5 ) )
% 3.59/1.85 & ( P3 @ ( proces988026546_ch2Of @ A @ Process4 ) @ ( proces988026546_ch2Of @ B @ Process5 ) ) ) ) ) ) )
% 3.59/1.85 => ( proces749077512rocess @ A @ B @ R @ X7 @ Y3 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_150_pred__equals__eq2,axiom,
% 3.59/1.85 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
% 3.59/1.85 ( ( ( ^ [X: A,Y5: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y5 ) @ R ) )
% 3.59/1.85 = ( ^ [X: A,Y5: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y5 ) @ S ) ) )
% 3.59/1.85 = ( R = S ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_151_internal__case__prod__conv,axiom,
% 3.59/1.85 ! [B: $tType,A: $tType,C: $tType,C3: B > C > A,A2: B,B2: C] :
% 3.59/1.85 ( ( produc2004651681e_prod @ B @ C @ A @ C3 @ ( product_Pair @ B @ C @ A2 @ B2 ) )
% 3.59/1.85 = ( C3 @ A2 @ B2 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_152_process_Orel__inject_I1_J,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,R: A > B > $o,X11: A,X122: proces634752977rocess @ A,Y11: B,Y12: proces634752977rocess @ B] :
% 3.59/1.85 ( ( proces749077512rocess @ A @ B @ R @ ( proces1525233512Action @ A @ X11 @ X122 ) @ ( proces1525233512Action @ B @ Y11 @ Y12 ) )
% 3.59/1.85 = ( ( R @ X11 @ Y11 )
% 3.59/1.85 & ( proces749077512rocess @ A @ B @ R @ X122 @ Y12 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_153_process_Orel__inject_I2_J,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,R: A > B > $o,X212: proces634752977rocess @ A,X223: proces634752977rocess @ A,Y21: proces634752977rocess @ B,Y22: proces634752977rocess @ B] :
% 3.59/1.85 ( ( proces749077512rocess @ A @ B @ R @ ( proces1915862579Choice @ A @ X212 @ X223 ) @ ( proces1915862579Choice @ B @ Y21 @ Y22 ) )
% 3.59/1.85 = ( ( proces749077512rocess @ A @ B @ R @ X212 @ Y21 )
% 3.59/1.85 & ( proces749077512rocess @ A @ B @ R @ X223 @ Y22 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_154_process_Orel__intros_I2_J,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,R: A > B > $o,X212: proces634752977rocess @ A,Y21: proces634752977rocess @ B,X223: proces634752977rocess @ A,Y22: proces634752977rocess @ B] :
% 3.59/1.85 ( ( proces749077512rocess @ A @ B @ R @ X212 @ Y21 )
% 3.59/1.85 => ( ( proces749077512rocess @ A @ B @ R @ X223 @ Y22 )
% 3.59/1.85 => ( proces749077512rocess @ A @ B @ R @ ( proces1915862579Choice @ A @ X212 @ X223 ) @ ( proces1915862579Choice @ B @ Y21 @ Y22 ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_155_process_Orel__refl,axiom,
% 3.59/1.85 ! [B: $tType,Ra: B > B > $o,X7: proces634752977rocess @ B] :
% 3.59/1.85 ( ! [X6: B] : ( Ra @ X6 @ X6 )
% 3.59/1.85 => ( proces749077512rocess @ B @ B @ Ra @ X7 @ X7 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_156_process_Orel__eq,axiom,
% 3.59/1.85 ! [A: $tType] :
% 3.59/1.85 ( ( proces749077512rocess @ A @ A
% 3.59/1.85 @ ^ [Y6: A,Z: A] : ( Y6 = Z ) )
% 3.59/1.85 = ( ^ [Y6: proces634752977rocess @ A,Z: proces634752977rocess @ A] : ( Y6 = Z ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_157_process_Orel__intros_I1_J,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,R: A > B > $o,X11: A,Y11: B,X122: proces634752977rocess @ A,Y12: proces634752977rocess @ B] :
% 3.59/1.85 ( ( R @ X11 @ Y11 )
% 3.59/1.85 => ( ( proces749077512rocess @ A @ B @ R @ X122 @ Y12 )
% 3.59/1.85 => ( proces749077512rocess @ A @ B @ R @ ( proces1525233512Action @ A @ X11 @ X122 ) @ ( proces1525233512Action @ B @ Y11 @ Y12 ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_158_process_Orel__distinct_I2_J,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,R: A > B > $o,Y21: proces634752977rocess @ A,Y22: proces634752977rocess @ A,X11: B,X122: proces634752977rocess @ B] :
% 3.59/1.85 ~ ( proces749077512rocess @ A @ B @ R @ ( proces1915862579Choice @ A @ Y21 @ Y22 ) @ ( proces1525233512Action @ B @ X11 @ X122 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_159_process_Orel__distinct_I1_J,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,R: A > B > $o,X11: A,X122: proces634752977rocess @ A,Y21: proces634752977rocess @ B,Y22: proces634752977rocess @ B] :
% 3.59/1.85 ~ ( proces749077512rocess @ A @ B @ R @ ( proces1525233512Action @ A @ X11 @ X122 ) @ ( proces1915862579Choice @ B @ Y21 @ Y22 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_160_process_Orel__cases,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,R: A > B > $o,A2: proces634752977rocess @ A,B2: proces634752977rocess @ B] :
% 3.59/1.85 ( ( proces749077512rocess @ A @ B @ R @ A2 @ B2 )
% 3.59/1.85 => ( ! [X13: A,X23: proces634752977rocess @ A] :
% 3.59/1.85 ( ( A2
% 3.59/1.85 = ( proces1525233512Action @ A @ X13 @ X23 ) )
% 3.59/1.85 => ! [Y13: B,Y23: proces634752977rocess @ B] :
% 3.59/1.85 ( ( B2
% 3.59/1.85 = ( proces1525233512Action @ B @ Y13 @ Y23 ) )
% 3.59/1.85 => ( ( R @ X13 @ Y13 )
% 3.59/1.85 => ~ ( proces749077512rocess @ A @ B @ R @ X23 @ Y23 ) ) ) )
% 3.59/1.85 => ~ ! [X1a: proces634752977rocess @ A,X2a: proces634752977rocess @ A] :
% 3.59/1.85 ( ( A2
% 3.59/1.85 = ( proces1915862579Choice @ A @ X1a @ X2a ) )
% 3.59/1.85 => ! [Y1a: proces634752977rocess @ B,Y2a: proces634752977rocess @ B] :
% 3.59/1.85 ( ( B2
% 3.59/1.85 = ( proces1915862579Choice @ B @ Y1a @ Y2a ) )
% 3.59/1.85 => ( ( proces749077512rocess @ A @ B @ R @ X1a @ Y1a )
% 3.59/1.85 => ~ ( proces749077512rocess @ A @ B @ R @ X2a @ Y2a ) ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_161_process__term_Orel__induct,axiom,
% 3.59/1.85 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X7: proces554692349s_term @ A @ Pvar,Y3: proces554692349s_term @ B @ C,Q: ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ B @ C ) > $o] :
% 3.59/1.85 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X7 @ Y3 )
% 3.59/1.85 => ( ! [A12: Pvar,B1: C] :
% 3.59/1.85 ( ( R22 @ A12 @ B1 )
% 3.59/1.85 => ( Q @ ( proces1627516585ss_VAR @ Pvar @ A @ A12 ) @ ( proces1627516585ss_VAR @ C @ B @ B1 ) ) )
% 3.59/1.85 => ( ! [A22: proces634752977rocess @ A,B22: proces634752977rocess @ B] :
% 3.59/1.85 ( ( proces749077512rocess @ A @ B @ R1 @ A22 @ B22 )
% 3.59/1.85 => ( Q @ ( proces1062592052s_PROC @ A @ Pvar @ A22 ) @ ( proces1062592052s_PROC @ B @ C @ B22 ) ) )
% 3.59/1.85 => ( ! [A31: A,A32: proces554692349s_term @ A @ Pvar,B31: B,B32: proces554692349s_term @ B @ C] :
% 3.59/1.85 ( ( R1 @ A31 @ B31 )
% 3.59/1.85 => ( ( Q @ A32 @ B32 )
% 3.59/1.85 => ( Q @ ( proces1454156180ss_ACT @ A @ Pvar @ A31 @ A32 ) @ ( proces1454156180ss_ACT @ B @ C @ B31 @ B32 ) ) ) )
% 3.59/1.85 => ( ! [A41: proces554692349s_term @ A @ Pvar,A42: proces554692349s_term @ A @ Pvar,B41: proces554692349s_term @ B @ C,B42: proces554692349s_term @ B @ C] :
% 3.59/1.85 ( ( Q @ A41 @ B41 )
% 3.59/1.85 => ( ( Q @ A42 @ B42 )
% 3.59/1.85 => ( Q @ ( proces89589571ess_CH @ A @ Pvar @ A41 @ A42 ) @ ( proces89589571ess_CH @ B @ C @ B41 @ B42 ) ) ) )
% 3.59/1.85 => ( Q @ X7 @ Y3 ) ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_162_process__term_Orel__cases,axiom,
% 3.59/1.85 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,A2: proces554692349s_term @ A @ Pvar,B2: proces554692349s_term @ B @ C] :
% 3.59/1.85 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ A2 @ B2 )
% 3.59/1.85 => ( ! [X6: Pvar] :
% 3.59/1.85 ( ( A2
% 3.59/1.85 = ( proces1627516585ss_VAR @ Pvar @ A @ X6 ) )
% 3.59/1.85 => ! [Y4: C] :
% 3.59/1.85 ( ( B2
% 3.59/1.85 = ( proces1627516585ss_VAR @ C @ B @ Y4 ) )
% 3.59/1.85 => ~ ( R22 @ X6 @ Y4 ) ) )
% 3.59/1.85 => ( ! [Xa2: proces634752977rocess @ A] :
% 3.59/1.85 ( ( A2
% 3.59/1.85 = ( proces1062592052s_PROC @ A @ Pvar @ Xa2 ) )
% 3.59/1.85 => ! [Ya: proces634752977rocess @ B] :
% 3.59/1.85 ( ( B2
% 3.59/1.85 = ( proces1062592052s_PROC @ B @ C @ Ya ) )
% 3.59/1.85 => ~ ( proces749077512rocess @ A @ B @ R1 @ Xa2 @ Ya ) ) )
% 3.59/1.85 => ( ! [X1a: A,X2a: proces554692349s_term @ A @ Pvar] :
% 3.59/1.85 ( ( A2
% 3.59/1.85 = ( proces1454156180ss_ACT @ A @ Pvar @ X1a @ X2a ) )
% 3.59/1.85 => ! [Y1a: B,Y2a: proces554692349s_term @ B @ C] :
% 3.59/1.85 ( ( B2
% 3.59/1.85 = ( proces1454156180ss_ACT @ B @ C @ Y1a @ Y2a ) )
% 3.59/1.85 => ( ( R1 @ X1a @ Y1a )
% 3.59/1.85 => ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X2a @ Y2a ) ) ) )
% 3.59/1.85 => ~ ! [X1b: proces554692349s_term @ A @ Pvar,X2b: proces554692349s_term @ A @ Pvar] :
% 3.59/1.85 ( ( A2
% 3.59/1.85 = ( proces89589571ess_CH @ A @ Pvar @ X1b @ X2b ) )
% 3.59/1.85 => ! [Y1b: proces554692349s_term @ B @ C,Y2b: proces554692349s_term @ B @ C] :
% 3.59/1.85 ( ( B2
% 3.59/1.85 = ( proces89589571ess_CH @ B @ C @ Y1b @ Y2b ) )
% 3.59/1.85 => ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X1b @ Y1b )
% 3.59/1.85 => ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X2b @ Y2b ) ) ) ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_163_process__term_Oset__cases_I2_J,axiom,
% 3.59/1.85 ! [Pvar: $tType,A: $tType,E3: Pvar,A2: proces554692349s_term @ A @ Pvar] :
% 3.59/1.85 ( ( member @ Pvar @ E3 @ ( proces1493547885s_term @ A @ Pvar @ A2 ) )
% 3.59/1.85 => ( ( A2
% 3.59/1.85 != ( proces1627516585ss_VAR @ Pvar @ A @ E3 ) )
% 3.59/1.85 => ( ! [Z1: A,Z2: proces554692349s_term @ A @ Pvar] :
% 3.59/1.85 ( ( A2
% 3.59/1.85 = ( proces1454156180ss_ACT @ A @ Pvar @ Z1 @ Z2 ) )
% 3.59/1.85 => ~ ( member @ Pvar @ E3 @ ( proces1493547885s_term @ A @ Pvar @ Z2 ) ) )
% 3.59/1.85 => ( ! [Z1: proces554692349s_term @ A @ Pvar] :
% 3.59/1.85 ( ? [Z2: proces554692349s_term @ A @ Pvar] :
% 3.59/1.85 ( A2
% 3.59/1.85 = ( proces89589571ess_CH @ A @ Pvar @ Z1 @ Z2 ) )
% 3.59/1.85 => ~ ( member @ Pvar @ E3 @ ( proces1493547885s_term @ A @ Pvar @ Z1 ) ) )
% 3.59/1.85 => ~ ! [Z1: proces554692349s_term @ A @ Pvar,Z2: proces554692349s_term @ A @ Pvar] :
% 3.59/1.85 ( ( A2
% 3.59/1.85 = ( proces89589571ess_CH @ A @ Pvar @ Z1 @ Z2 ) )
% 3.59/1.85 => ~ ( member @ Pvar @ E3 @ ( proces1493547885s_term @ A @ Pvar @ Z2 ) ) ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_164_process__term_Oset__intros_I6_J,axiom,
% 3.59/1.85 ! [A: $tType,Pvar: $tType,Ab2: Pvar] : ( member @ Pvar @ Ab2 @ ( proces1493547885s_term @ A @ Pvar @ ( proces1627516585ss_VAR @ Pvar @ A @ Ab2 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_165_process__term_Oset__intros_I8_J,axiom,
% 3.59/1.85 ! [Pvar: $tType,A: $tType,Xk: Pvar,A1c: proces554692349s_term @ A @ Pvar,A2c: proces554692349s_term @ A @ Pvar] :
% 3.59/1.85 ( ( member @ Pvar @ Xk @ ( proces1493547885s_term @ A @ Pvar @ A1c ) )
% 3.59/1.85 => ( member @ Pvar @ Xk @ ( proces1493547885s_term @ A @ Pvar @ ( proces89589571ess_CH @ A @ Pvar @ A1c @ A2c ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_166_process__term_Oset__intros_I9_J,axiom,
% 3.59/1.85 ! [Pvar: $tType,A: $tType,Xm: Pvar,A2c: proces554692349s_term @ A @ Pvar,A1c: proces554692349s_term @ A @ Pvar] :
% 3.59/1.85 ( ( member @ Pvar @ Xm @ ( proces1493547885s_term @ A @ Pvar @ A2c ) )
% 3.59/1.85 => ( member @ Pvar @ Xm @ ( proces1493547885s_term @ A @ Pvar @ ( proces89589571ess_CH @ A @ Pvar @ A1c @ A2c ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_167_process__term_Oset__intros_I7_J,axiom,
% 3.59/1.85 ! [Pvar: $tType,A: $tType,Xi: Pvar,A2b: proces554692349s_term @ A @ Pvar,A1b: A] :
% 3.59/1.85 ( ( member @ Pvar @ Xi @ ( proces1493547885s_term @ A @ Pvar @ A2b ) )
% 3.59/1.85 => ( member @ Pvar @ Xi @ ( proces1493547885s_term @ A @ Pvar @ ( proces1454156180ss_ACT @ A @ Pvar @ A1b @ A2b ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_168_process__term_Osimps_I51_J,axiom,
% 3.59/1.85 ! [Pvar: $tType,A: $tType,X31: A,X32: proces554692349s_term @ A @ Pvar] :
% 3.59/1.85 ( ( proces1493547885s_term @ A @ Pvar @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) )
% 3.59/1.85 = ( proces1493547885s_term @ A @ Pvar @ X32 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_169_process__term_Orel__intros_I1_J,axiom,
% 3.59/1.85 ! [Pvar: $tType,A: $tType,B: $tType,C: $tType,R22: Pvar > C > $o,X1: Pvar,Y1: C,R1: A > B > $o] :
% 3.59/1.85 ( ( R22 @ X1 @ Y1 )
% 3.59/1.85 => ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) @ ( proces1627516585ss_VAR @ C @ B @ Y1 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_170_process__term_Orel__inject_I1_J,axiom,
% 3.59/1.85 ! [B: $tType,A: $tType,Pvar: $tType,C: $tType,R1: A > B > $o,R22: Pvar > C > $o,X1: Pvar,Y1: C] :
% 3.59/1.85 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) @ ( proces1627516585ss_VAR @ C @ B @ Y1 ) )
% 3.59/1.85 = ( R22 @ X1 @ Y1 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_171_process__term_Orel__intros_I4_J,axiom,
% 3.59/1.85 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X41: proces554692349s_term @ A @ Pvar,Y41: proces554692349s_term @ B @ C,X42: proces554692349s_term @ A @ Pvar,Y42: proces554692349s_term @ B @ C] :
% 3.59/1.85 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X41 @ Y41 )
% 3.59/1.85 => ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X42 @ Y42 )
% 3.59/1.85 => ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_172_process__term_Orel__inject_I4_J,axiom,
% 3.59/1.85 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X41: proces554692349s_term @ A @ Pvar,X42: proces554692349s_term @ A @ Pvar,Y41: proces554692349s_term @ B @ C,Y42: proces554692349s_term @ B @ C] :
% 3.59/1.85 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces89589571ess_CH @ A @ Pvar @ X41 @ X42 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) )
% 3.59/1.85 = ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X41 @ Y41 )
% 3.59/1.85 & ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X42 @ Y42 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_173_process__term_Orel__intros_I3_J,axiom,
% 3.59/1.85 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,X31: A,Y31: B,R22: Pvar > C > $o,X32: proces554692349s_term @ A @ Pvar,Y32: proces554692349s_term @ B @ C] :
% 3.59/1.85 ( ( R1 @ X31 @ Y31 )
% 3.59/1.85 => ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X32 @ Y32 )
% 3.59/1.85 => ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_174_process__term_Orel__inject_I3_J,axiom,
% 3.59/1.85 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X31: A,X32: proces554692349s_term @ A @ Pvar,Y31: B,Y32: proces554692349s_term @ B @ C] :
% 3.59/1.85 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) )
% 3.59/1.85 = ( ( R1 @ X31 @ Y31 )
% 3.59/1.85 & ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ X32 @ Y32 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_175_process__term_Orel__eq,axiom,
% 3.59/1.85 ! [B: $tType,A: $tType] :
% 3.59/1.85 ( ( proces2029722208s_term @ A @ A @ B @ B
% 3.59/1.85 @ ^ [Y6: A,Z: A] : ( Y6 = Z )
% 3.59/1.85 @ ^ [Y6: B,Z: B] : ( Y6 = Z ) )
% 3.59/1.85 = ( ^ [Y6: proces554692349s_term @ A @ B,Z: proces554692349s_term @ A @ B] : ( Y6 = Z ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_176_process__term_Orel__refl,axiom,
% 3.59/1.85 ! [D: $tType,C: $tType,R1a: C > C > $o,R2a: D > D > $o,X7: proces554692349s_term @ C @ D] :
% 3.59/1.85 ( ! [X6: C] : ( R1a @ X6 @ X6 )
% 3.59/1.85 => ( ! [X6: D] : ( R2a @ X6 @ X6 )
% 3.59/1.85 => ( proces2029722208s_term @ C @ C @ D @ D @ R1a @ R2a @ X7 @ X7 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_177_process__term_Orel__inject_I2_J,axiom,
% 3.59/1.85 ! [C: $tType,Pvar: $tType,A: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X2: proces634752977rocess @ A,Y2: proces634752977rocess @ B] :
% 3.59/1.85 ( ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) @ ( proces1062592052s_PROC @ B @ C @ Y2 ) )
% 3.59/1.85 = ( proces749077512rocess @ A @ B @ R1 @ X2 @ Y2 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_178_process__term_Orel__intros_I2_J,axiom,
% 3.59/1.85 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,X2: proces634752977rocess @ A,Y2: proces634752977rocess @ B,R22: Pvar > C > $o] :
% 3.59/1.85 ( ( proces749077512rocess @ A @ B @ R1 @ X2 @ Y2 )
% 3.59/1.85 => ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) @ ( proces1062592052s_PROC @ B @ C @ Y2 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_179_process__term_Orel__distinct_I1_J,axiom,
% 3.59/1.85 ! [Pvar: $tType,A: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X1: Pvar,Y2: proces634752977rocess @ B] :
% 3.59/1.85 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) @ ( proces1062592052s_PROC @ B @ C @ Y2 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_180_process__term_Orel__distinct_I2_J,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,C: $tType,D: $tType,R1: A > C > $o,R22: B > D > $o,Y2: proces634752977rocess @ A,X1: D] :
% 3.59/1.85 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ B @ Y2 ) @ ( proces1627516585ss_VAR @ D @ C @ X1 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_181_process__term_Orel__distinct_I9_J,axiom,
% 3.59/1.85 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X2: proces634752977rocess @ A,Y41: proces554692349s_term @ B @ C,Y42: proces554692349s_term @ B @ C] :
% 3.59/1.85 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_182_process__term_Orel__distinct_I10_J,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: B > D > $o,Y41: proces554692349s_term @ A @ B,Y42: proces554692349s_term @ A @ B,X2: proces634752977rocess @ C] :
% 3.59/1.85 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces89589571ess_CH @ A @ B @ Y41 @ Y42 ) @ ( proces1062592052s_PROC @ C @ D @ X2 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_183_process__term_Orel__distinct_I7_J,axiom,
% 3.59/1.85 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X2: proces634752977rocess @ A,Y31: B,Y32: proces554692349s_term @ B @ C] :
% 3.59/1.85 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1062592052s_PROC @ A @ Pvar @ X2 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_184_process__term_Orel__distinct_I8_J,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: B > D > $o,Y31: A,Y32: proces554692349s_term @ A @ B,X2: proces634752977rocess @ C] :
% 3.59/1.85 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ B @ Y31 @ Y32 ) @ ( proces1062592052s_PROC @ C @ D @ X2 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_185_process__term_Orel__distinct_I6_J,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,C: $tType,D: $tType,R1: A > C > $o,R22: B > D > $o,Y41: proces554692349s_term @ A @ B,Y42: proces554692349s_term @ A @ B,X1: D] :
% 3.59/1.85 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces89589571ess_CH @ A @ B @ Y41 @ Y42 ) @ ( proces1627516585ss_VAR @ D @ C @ X1 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_186_process__term_Orel__distinct_I5_J,axiom,
% 3.59/1.85 ! [Pvar: $tType,A: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X1: Pvar,Y41: proces554692349s_term @ B @ C,Y42: proces554692349s_term @ B @ C] :
% 3.59/1.85 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_187_process__term_Orel__distinct_I4_J,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,C: $tType,D: $tType,R1: A > C > $o,R22: B > D > $o,Y31: A,Y32: proces554692349s_term @ A @ B,X1: D] :
% 3.59/1.85 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ B @ Y31 @ Y32 ) @ ( proces1627516585ss_VAR @ D @ C @ X1 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_188_process__term_Orel__distinct_I3_J,axiom,
% 3.59/1.85 ! [Pvar: $tType,A: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X1: Pvar,Y31: B,Y32: proces554692349s_term @ B @ C] :
% 3.59/1.85 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1627516585ss_VAR @ Pvar @ A @ X1 ) @ ( proces1454156180ss_ACT @ B @ C @ Y31 @ Y32 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_189_process__term_Orel__distinct_I12_J,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: B > D > $o,Y41: proces554692349s_term @ A @ B,Y42: proces554692349s_term @ A @ B,X31: C,X32: proces554692349s_term @ C @ D] :
% 3.59/1.85 ~ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 @ ( proces89589571ess_CH @ A @ B @ Y41 @ Y42 ) @ ( proces1454156180ss_ACT @ C @ D @ X31 @ X32 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_190_process__term_Orel__distinct_I11_J,axiom,
% 3.59/1.85 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o,X31: A,X32: proces554692349s_term @ A @ Pvar,Y41: proces554692349s_term @ B @ C,Y42: proces554692349s_term @ B @ C] :
% 3.59/1.85 ~ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 @ ( proces1454156180ss_ACT @ A @ Pvar @ X31 @ X32 ) @ ( proces89589571ess_CH @ B @ C @ Y41 @ Y42 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_191_accp_Ocases,axiom,
% 3.59/1.85 ! [A: $tType,R3: A > A > $o,A2: A] :
% 3.59/1.85 ( ( accp @ A @ R3 @ A2 )
% 3.59/1.85 => ! [Y7: A] :
% 3.59/1.85 ( ( R3 @ Y7 @ A2 )
% 3.59/1.85 => ( accp @ A @ R3 @ Y7 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_192_accp_Osimps,axiom,
% 3.59/1.85 ! [A: $tType] :
% 3.59/1.85 ( ( accp @ A )
% 3.59/1.85 = ( ^ [R4: A > A > $o,A5: A] :
% 3.59/1.85 ? [X: A] :
% 3.59/1.85 ( ( A5 = X )
% 3.59/1.85 & ! [Y5: A] :
% 3.59/1.85 ( ( R4 @ Y5 @ X )
% 3.59/1.85 => ( accp @ A @ R4 @ Y5 ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_193_accp_Ointros,axiom,
% 3.59/1.85 ! [A: $tType,R3: A > A > $o,X7: A] :
% 3.59/1.85 ( ! [Y4: A] :
% 3.59/1.85 ( ( R3 @ Y4 @ X7 )
% 3.59/1.85 => ( accp @ A @ R3 @ Y4 ) )
% 3.59/1.85 => ( accp @ A @ R3 @ X7 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_194_accp__induct__rule,axiom,
% 3.59/1.85 ! [A: $tType,R3: A > A > $o,A2: A,P3: A > $o] :
% 3.59/1.85 ( ( accp @ A @ R3 @ A2 )
% 3.59/1.85 => ( ! [X6: A] :
% 3.59/1.85 ( ( accp @ A @ R3 @ X6 )
% 3.59/1.85 => ( ! [Y7: A] :
% 3.59/1.85 ( ( R3 @ Y7 @ X6 )
% 3.59/1.85 => ( P3 @ Y7 ) )
% 3.59/1.85 => ( P3 @ X6 ) ) )
% 3.59/1.85 => ( P3 @ A2 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_195_not__accp__down,axiom,
% 3.59/1.85 ! [A: $tType,R: A > A > $o,X7: A] :
% 3.59/1.85 ( ~ ( accp @ A @ R @ X7 )
% 3.59/1.85 => ~ ! [Z3: A] :
% 3.59/1.85 ( ( R @ Z3 @ X7 )
% 3.59/1.85 => ( accp @ A @ R @ Z3 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_196_accp__downward,axiom,
% 3.59/1.85 ! [A: $tType,R3: A > A > $o,B2: A,A2: A] :
% 3.59/1.85 ( ( accp @ A @ R3 @ B2 )
% 3.59/1.85 => ( ( R3 @ A2 @ B2 )
% 3.59/1.85 => ( accp @ A @ R3 @ A2 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_197_accp_Oinducts,axiom,
% 3.59/1.85 ! [A: $tType,R3: A > A > $o,X7: A,P3: A > $o] :
% 3.59/1.85 ( ( accp @ A @ R3 @ X7 )
% 3.59/1.85 => ( ! [X6: A] :
% 3.59/1.85 ( ! [Y7: A] :
% 3.59/1.85 ( ( R3 @ Y7 @ X6 )
% 3.59/1.85 => ( accp @ A @ R3 @ Y7 ) )
% 3.59/1.85 => ( ! [Y7: A] :
% 3.59/1.85 ( ( R3 @ Y7 @ X6 )
% 3.59/1.85 => ( P3 @ Y7 ) )
% 3.59/1.85 => ( P3 @ X6 ) ) )
% 3.59/1.85 => ( P3 @ X7 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_198_accp__induct,axiom,
% 3.59/1.85 ! [A: $tType,R3: A > A > $o,A2: A,P3: A > $o] :
% 3.59/1.85 ( ( accp @ A @ R3 @ A2 )
% 3.59/1.85 => ( ! [X6: A] :
% 3.59/1.85 ( ( accp @ A @ R3 @ X6 )
% 3.59/1.85 => ( ! [Y7: A] :
% 3.59/1.85 ( ( R3 @ Y7 @ X6 )
% 3.59/1.85 => ( P3 @ Y7 ) )
% 3.59/1.85 => ( P3 @ X6 ) ) )
% 3.59/1.85 => ( P3 @ A2 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_199_in__lex__prod,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,A2: A,B2: B,A6: A,B3: B,R3: set @ ( product_prod @ A @ A ),S2: set @ ( product_prod @ B @ B )] :
% 3.59/1.85 ( ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A2 @ B2 ) @ ( product_Pair @ A @ B @ A6 @ B3 ) ) @ ( lex_prod @ A @ B @ R3 @ S2 ) )
% 3.59/1.85 = ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ A6 ) @ R3 )
% 3.59/1.85 | ( ( A2 = A6 )
% 3.59/1.85 & ( member @ ( product_prod @ B @ B ) @ ( product_Pair @ B @ B @ B2 @ B3 ) @ S2 ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_200_process_Ocorec__code,axiom,
% 3.59/1.85 ! [A: $tType,C: $tType] :
% 3.59/1.85 ( ( proces894737309rocess @ C @ A )
% 3.59/1.85 = ( ^ [P5: C > $o,G11: C > A,Q12: C > $o,G121: C > ( proces634752977rocess @ A ),G122: C > C,Q21: C > $o,G211: C > ( proces634752977rocess @ A ),G212: C > C,Q22: C > $o,G221: C > ( proces634752977rocess @ A ),G222: C > C,A5: C] : ( if @ ( proces634752977rocess @ A ) @ ( P5 @ A5 ) @ ( proces1525233512Action @ A @ ( G11 @ A5 ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q12 @ A5 ) @ ( G121 @ A5 ) @ ( proces894737309rocess @ C @ A @ P5 @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G122 @ A5 ) ) ) ) @ ( proces1915862579Choice @ A @ ( if @ ( proces634752977rocess @ A ) @ ( Q21 @ A5 ) @ ( G211 @ A5 ) @ ( proces894737309rocess @ C @ A @ P5 @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G212 @ A5 ) ) ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q22 @ A5 ) @ ( G221 @ A5 ) @ ( proces894737309rocess @ C @ A @ P5 @ G11 @ Q12 @ G121 @ G122 @ Q21 @ G211 @ G212 @ Q22 @ G221 @ G222 @ ( G222 @ A5 ) ) ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_201_process_Ocorec__disc__iff_I1_J,axiom,
% 3.59/1.85 ! [A: $tType,C: $tType,P: C > $o,G112: C > A,Q122: C > $o,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,Q212: C > $o,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,Q222: C > $o,G2212: C > ( proces634752977rocess @ A ),G2222: C > C,A2: C] :
% 3.59/1.85 ( ( proces10484146Action @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 3.59/1.85 = ( P @ A2 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_202_process_Ocorec__disc__iff_I2_J,axiom,
% 3.59/1.85 ! [A: $tType,C: $tType,P: C > $o,G112: C > A,Q122: C > $o,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,Q212: C > $o,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,Q222: C > $o,G2212: C > ( proces634752977rocess @ A ),G2222: C > C,A2: C] :
% 3.59/1.85 ( ( proces401113213Choice @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 3.59/1.85 = ( ~ ( P @ A2 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_203_process_Ocorec__disc_I1_J,axiom,
% 3.59/1.85 ! [A: $tType,C: $tType,P: C > $o,A2: C,G112: C > A,Q122: C > $o,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,Q212: C > $o,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,Q222: C > $o,G2212: C > ( proces634752977rocess @ A ),G2222: C > C] :
% 3.59/1.85 ( ( P @ A2 )
% 3.59/1.85 => ( proces10484146Action @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_204_process_Ocorec_I1_J,axiom,
% 3.59/1.85 ! [A: $tType,C: $tType,P: C > $o,A2: C,G112: C > A,Q122: C > $o,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,Q212: C > $o,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,Q222: C > $o,G2212: C > ( proces634752977rocess @ A ),G2222: C > C] :
% 3.59/1.85 ( ( P @ A2 )
% 3.59/1.85 => ( ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 )
% 3.59/1.85 = ( proces1525233512Action @ A @ ( G112 @ A2 ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q122 @ A2 ) @ ( G1212 @ A2 ) @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G1222 @ A2 ) ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_205_process_Ocorec_I2_J,axiom,
% 3.59/1.85 ! [A: $tType,C: $tType,P: C > $o,A2: C,G112: C > A,Q122: C > $o,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,Q212: C > $o,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,Q222: C > $o,G2212: C > ( proces634752977rocess @ A ),G2222: C > C] :
% 3.59/1.85 ( ~ ( P @ A2 )
% 3.59/1.85 => ( ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 )
% 3.59/1.85 = ( proces1915862579Choice @ A @ ( if @ ( proces634752977rocess @ A ) @ ( Q212 @ A2 ) @ ( G2112 @ A2 ) @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G2122 @ A2 ) ) ) @ ( if @ ( proces634752977rocess @ A ) @ ( Q222 @ A2 ) @ ( G2212 @ A2 ) @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G2222 @ A2 ) ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_206_process_Ocorec__disc_I2_J,axiom,
% 3.59/1.85 ! [A: $tType,C: $tType,P: C > $o,A2: C,G112: C > A,Q122: C > $o,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,Q212: C > $o,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,Q222: C > $o,G2212: C > ( proces634752977rocess @ A ),G2222: C > C] :
% 3.59/1.85 ( ~ ( P @ A2 )
% 3.59/1.85 => ( proces401113213Choice @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_207_process_Ocorec__sel_I2_J,axiom,
% 3.59/1.85 ! [A: $tType,C: $tType,P: C > $o,A2: C,Q122: C > $o,G112: C > A,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,Q212: C > $o,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,Q222: C > $o,G2212: C > ( proces634752977rocess @ A ),G2222: C > C] :
% 3.59/1.85 ( ( P @ A2 )
% 3.59/1.85 => ( ( ( Q122 @ A2 )
% 3.59/1.85 => ( ( proces1778668539contOf @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 3.59/1.85 = ( G1212 @ A2 ) ) )
% 3.59/1.85 & ( ~ ( Q122 @ A2 )
% 3.59/1.85 => ( ( proces1778668539contOf @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 3.59/1.85 = ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G1222 @ A2 ) ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_208_process_Ocorec__sel_I3_J,axiom,
% 3.59/1.85 ! [A: $tType,C: $tType,P: C > $o,A2: C,Q212: C > $o,G112: C > A,Q122: C > $o,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,Q222: C > $o,G2212: C > ( proces634752977rocess @ A ),G2222: C > C] :
% 3.59/1.85 ( ~ ( P @ A2 )
% 3.59/1.85 => ( ( ( Q212 @ A2 )
% 3.59/1.85 => ( ( proces979765041_ch1Of @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 3.59/1.85 = ( G2112 @ A2 ) ) )
% 3.59/1.85 & ( ~ ( Q212 @ A2 )
% 3.59/1.85 => ( ( proces979765041_ch1Of @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 3.59/1.85 = ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G2122 @ A2 ) ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_209_process_Ocorec__sel_I4_J,axiom,
% 3.59/1.85 ! [A: $tType,C: $tType,P: C > $o,A2: C,Q222: C > $o,G112: C > A,Q122: C > $o,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,Q212: C > $o,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,G2212: C > ( proces634752977rocess @ A ),G2222: C > C] :
% 3.59/1.85 ( ~ ( P @ A2 )
% 3.59/1.85 => ( ( ( Q222 @ A2 )
% 3.59/1.85 => ( ( proces988026546_ch2Of @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 3.59/1.85 = ( G2212 @ A2 ) ) )
% 3.59/1.85 & ( ~ ( Q222 @ A2 )
% 3.59/1.85 => ( ( proces988026546_ch2Of @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 3.59/1.85 = ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ ( G2222 @ A2 ) ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_210_process_Ocorec__sel_I1_J,axiom,
% 3.59/1.85 ! [A: $tType,C: $tType,P: C > $o,A2: C,G112: C > A,Q122: C > $o,G1212: C > ( proces634752977rocess @ A ),G1222: C > C,Q212: C > $o,G2112: C > ( proces634752977rocess @ A ),G2122: C > C,Q222: C > $o,G2212: C > ( proces634752977rocess @ A ),G2222: C > C] :
% 3.59/1.85 ( ( P @ A2 )
% 3.59/1.85 => ( ( proces745025900prefOf @ A @ ( proces894737309rocess @ C @ A @ P @ G112 @ Q122 @ G1212 @ G1222 @ Q212 @ G2112 @ G2122 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 3.59/1.85 = ( G112 @ A2 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_211_same__fstI,axiom,
% 3.59/1.85 ! [B: $tType,A: $tType,P3: A > $o,X7: A,Y8: B,Y3: B,R: A > ( set @ ( product_prod @ B @ B ) )] :
% 3.59/1.85 ( ( P3 @ X7 )
% 3.59/1.85 => ( ( member @ ( product_prod @ B @ B ) @ ( product_Pair @ B @ B @ Y8 @ Y3 ) @ ( R @ X7 ) )
% 3.59/1.85 => ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X7 @ Y8 ) @ ( product_Pair @ A @ B @ X7 @ Y3 ) ) @ ( same_fst @ A @ B @ P3 @ R ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_212_ssubst__Pair__rhs,axiom,
% 3.59/1.85 ! [B: $tType,A: $tType,R3: A,S2: B,R: set @ ( product_prod @ A @ B ),S3: B] :
% 3.59/1.85 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R3 @ S2 ) @ R )
% 3.59/1.85 => ( ( S3 = S2 )
% 3.59/1.85 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R3 @ S3 ) @ R ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_213_cut__def,axiom,
% 3.59/1.85 ! [B: $tType,A: $tType] :
% 3.59/1.85 ( ( cut @ A @ B )
% 3.59/1.85 = ( ^ [F7: A > B,R2: set @ ( product_prod @ A @ A ),X: A,Y5: A] : ( if @ B @ ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y5 @ X ) @ R2 ) @ ( F7 @ Y5 ) @ ( undefined @ B ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_214_curry__conv,axiom,
% 3.59/1.85 ! [A: $tType,C: $tType,B: $tType] :
% 3.59/1.85 ( ( product_curry @ B @ C @ A )
% 3.59/1.85 = ( ^ [F7: ( product_prod @ B @ C ) > A,A5: B,B5: C] : ( F7 @ ( product_Pair @ B @ C @ A5 @ B5 ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_215_curryI,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,F: ( product_prod @ A @ B ) > $o,A2: A,B2: B] :
% 3.59/1.85 ( ( F @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 3.59/1.85 => ( product_curry @ A @ B @ $o @ F @ A2 @ B2 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_216_cuts__eq,axiom,
% 3.59/1.85 ! [B: $tType,A: $tType,F: A > B,R: set @ ( product_prod @ A @ A ),X7: A,G: A > B] :
% 3.59/1.85 ( ( ( cut @ A @ B @ F @ R @ X7 )
% 3.59/1.85 = ( cut @ A @ B @ G @ R @ X7 ) )
% 3.59/1.85 = ( ! [Y5: A] :
% 3.59/1.85 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y5 @ X7 ) @ R )
% 3.59/1.85 => ( ( F @ Y5 )
% 3.59/1.85 = ( G @ Y5 ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_217_cut__apply,axiom,
% 3.59/1.85 ! [B: $tType,A: $tType,X7: A,A2: A,R: set @ ( product_prod @ A @ A ),F: A > B] :
% 3.59/1.85 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X7 @ A2 ) @ R )
% 3.59/1.85 => ( ( cut @ A @ B @ F @ R @ A2 @ X7 )
% 3.59/1.85 = ( F @ X7 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_218_curry__K,axiom,
% 3.59/1.85 ! [B: $tType,C: $tType,A: $tType,C3: C] :
% 3.59/1.85 ( ( product_curry @ A @ B @ C
% 3.59/1.85 @ ^ [X: product_prod @ A @ B] : C3 )
% 3.59/1.85 = ( ^ [X: A,Y5: B] : C3 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_219_curryD,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,F: ( product_prod @ A @ B ) > $o,A2: A,B2: B] :
% 3.59/1.85 ( ( product_curry @ A @ B @ $o @ F @ A2 @ B2 )
% 3.59/1.85 => ( F @ ( product_Pair @ A @ B @ A2 @ B2 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_220_curryE,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,F: ( product_prod @ A @ B ) > $o,A2: A,B2: B] :
% 3.59/1.85 ( ( product_curry @ A @ B @ $o @ F @ A2 @ B2 )
% 3.59/1.85 => ( F @ ( product_Pair @ A @ B @ A2 @ B2 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_221_curry__def,axiom,
% 3.59/1.85 ! [C: $tType,B: $tType,A: $tType] :
% 3.59/1.85 ( ( product_curry @ A @ B @ C )
% 3.59/1.85 = ( ^ [C4: ( product_prod @ A @ B ) > C,X: A,Y5: B] : ( C4 @ ( product_Pair @ A @ B @ X @ Y5 ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_222_adm__lemma,axiom,
% 3.59/1.85 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ A ),F8: ( A > B ) > A > B] :
% 3.59/1.85 ( adm_wf @ A @ B @ R
% 3.59/1.85 @ ^ [F7: A > B,X: A] : ( F8 @ ( cut @ A @ B @ F7 @ R @ X ) @ X ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_223_accp__acc__eq,axiom,
% 3.59/1.85 ! [A: $tType,R3: set @ ( product_prod @ A @ A )] :
% 3.59/1.85 ( ( accp @ A
% 3.59/1.85 @ ^ [X: A,Y5: A] : ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y5 ) @ R3 ) )
% 3.59/1.85 = ( ^ [X: A] : ( member @ A @ X @ ( acc @ A @ R3 ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_224_acc_Ocases,axiom,
% 3.59/1.85 ! [A: $tType,A2: A,R3: set @ ( product_prod @ A @ A )] :
% 3.59/1.85 ( ( member @ A @ A2 @ ( acc @ A @ R3 ) )
% 3.59/1.85 => ! [Y7: A] :
% 3.59/1.85 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y7 @ A2 ) @ R3 )
% 3.59/1.85 => ( member @ A @ Y7 @ ( acc @ A @ R3 ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_225_acc_Osimps,axiom,
% 3.59/1.85 ! [A: $tType,A2: A,R3: set @ ( product_prod @ A @ A )] :
% 3.59/1.85 ( ( member @ A @ A2 @ ( acc @ A @ R3 ) )
% 3.59/1.85 = ( ? [X: A] :
% 3.59/1.85 ( ( A2 = X )
% 3.59/1.85 & ! [Y5: A] :
% 3.59/1.85 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y5 @ X ) @ R3 )
% 3.59/1.85 => ( member @ A @ Y5 @ ( acc @ A @ R3 ) ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_226_acc_Ointros,axiom,
% 3.59/1.85 ! [A: $tType,X7: A,R3: set @ ( product_prod @ A @ A )] :
% 3.59/1.85 ( ! [Y4: A] :
% 3.59/1.85 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y4 @ X7 ) @ R3 )
% 3.59/1.85 => ( member @ A @ Y4 @ ( acc @ A @ R3 ) ) )
% 3.59/1.85 => ( member @ A @ X7 @ ( acc @ A @ R3 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_227_acc__induct,axiom,
% 3.59/1.85 ! [A: $tType,A2: A,R3: set @ ( product_prod @ A @ A ),P3: A > $o] :
% 3.59/1.85 ( ( member @ A @ A2 @ ( acc @ A @ R3 ) )
% 3.59/1.85 => ( ! [X6: A] :
% 3.59/1.85 ( ( member @ A @ X6 @ ( acc @ A @ R3 ) )
% 3.59/1.85 => ( ! [Y7: A] :
% 3.59/1.85 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y7 @ X6 ) @ R3 )
% 3.59/1.85 => ( P3 @ Y7 ) )
% 3.59/1.85 => ( P3 @ X6 ) ) )
% 3.59/1.85 => ( P3 @ A2 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_228_acc_Oinducts,axiom,
% 3.59/1.85 ! [A: $tType,X7: A,R3: set @ ( product_prod @ A @ A ),P3: A > $o] :
% 3.59/1.85 ( ( member @ A @ X7 @ ( acc @ A @ R3 ) )
% 3.59/1.85 => ( ! [X6: A] :
% 3.59/1.85 ( ! [Y7: A] :
% 3.59/1.85 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y7 @ X6 ) @ R3 )
% 3.59/1.85 => ( member @ A @ Y7 @ ( acc @ A @ R3 ) ) )
% 3.59/1.85 => ( ! [Y7: A] :
% 3.59/1.85 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y7 @ X6 ) @ R3 )
% 3.59/1.85 => ( P3 @ Y7 ) )
% 3.59/1.85 => ( P3 @ X6 ) ) )
% 3.59/1.85 => ( P3 @ X7 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_229_acc__downward,axiom,
% 3.59/1.85 ! [A: $tType,B2: A,R3: set @ ( product_prod @ A @ A ),A2: A] :
% 3.59/1.85 ( ( member @ A @ B2 @ ( acc @ A @ R3 ) )
% 3.59/1.85 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ R3 )
% 3.59/1.85 => ( member @ A @ A2 @ ( acc @ A @ R3 ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_230_not__acc__down,axiom,
% 3.59/1.85 ! [A: $tType,X7: A,R: set @ ( product_prod @ A @ A )] :
% 3.59/1.85 ( ~ ( member @ A @ X7 @ ( acc @ A @ R ) )
% 3.59/1.85 => ~ ! [Z3: A] :
% 3.59/1.85 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Z3 @ X7 ) @ R )
% 3.59/1.85 => ( member @ A @ Z3 @ ( acc @ A @ R ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_231_acc__induct__rule,axiom,
% 3.59/1.85 ! [A: $tType,A2: A,R3: set @ ( product_prod @ A @ A ),P3: A > $o] :
% 3.59/1.85 ( ( member @ A @ A2 @ ( acc @ A @ R3 ) )
% 3.59/1.85 => ( ! [X6: A] :
% 3.59/1.85 ( ( member @ A @ X6 @ ( acc @ A @ R3 ) )
% 3.59/1.85 => ( ! [Y7: A] :
% 3.59/1.85 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Y7 @ X6 ) @ R3 )
% 3.59/1.85 => ( P3 @ Y7 ) )
% 3.59/1.85 => ( P3 @ X6 ) ) )
% 3.59/1.85 => ( P3 @ A2 ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_232_adm__wf__def,axiom,
% 3.59/1.85 ! [B: $tType,A: $tType] :
% 3.59/1.85 ( ( adm_wf @ A @ B )
% 3.59/1.85 = ( ^ [R2: set @ ( product_prod @ A @ A ),F9: ( A > B ) > A > B] :
% 3.59/1.85 ! [F7: A > B,G4: A > B,X: A] :
% 3.59/1.85 ( ! [Z4: A] :
% 3.59/1.85 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ Z4 @ X ) @ R2 )
% 3.59/1.85 => ( ( F7 @ Z4 )
% 3.59/1.85 = ( G4 @ Z4 ) ) )
% 3.59/1.85 => ( ( F9 @ F7 @ X )
% 3.59/1.85 = ( F9 @ G4 @ X ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_233_acc__def,axiom,
% 3.59/1.85 ! [A: $tType] :
% 3.59/1.85 ( ( acc @ A )
% 3.59/1.85 = ( ^ [R4: set @ ( product_prod @ A @ A )] :
% 3.59/1.85 ( collect @ A
% 3.59/1.85 @ ( accp @ A
% 3.59/1.85 @ ^ [X: A,Y5: A] : ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y5 ) @ R4 ) ) ) ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_234_process__term_Octr__transfer_I2_J,axiom,
% 3.59/1.85 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o] : ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( proces749077512rocess @ A @ B @ R1 ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( proces1062592052s_PROC @ A @ Pvar ) @ ( proces1062592052s_PROC @ B @ C ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_235_in__inv__image,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,X7: A,Y3: A,R3: set @ ( product_prod @ B @ B ),F: A > B] :
% 3.59/1.85 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X7 @ Y3 ) @ ( inv_image @ B @ A @ R3 @ F ) )
% 3.59/1.85 = ( member @ ( product_prod @ B @ B ) @ ( product_Pair @ B @ B @ ( F @ X7 ) @ ( F @ Y3 ) ) @ R3 ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_236_process__term_Octr__transfer_I1_J,axiom,
% 3.59/1.85 ! [Pvar: $tType,A: $tType,B: $tType,C: $tType,R22: Pvar > C > $o,R1: A > B > $o] : ( bNF_rel_fun @ Pvar @ C @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ R22 @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( proces1627516585ss_VAR @ Pvar @ A ) @ ( proces1627516585ss_VAR @ C @ B ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_237_process__term_Orec__transfer,axiom,
% 3.59/1.85 ! [Pvar: $tType,D: $tType,A: $tType,B: $tType,E: $tType,C: $tType,R22: Pvar > C > $o,S: D > E > $o,R1: A > B > $o] : ( bNF_rel_fun @ ( Pvar > D ) @ ( C > E ) @ ( ( ( proces634752977rocess @ A ) > D ) > ( A > ( proces554692349s_term @ A @ Pvar ) > D > D ) > ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( ( proces634752977rocess @ B ) > E ) > ( B > ( proces554692349s_term @ B @ C ) > E > E ) > ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E > E > E ) > ( proces554692349s_term @ B @ C ) > E ) @ ( bNF_rel_fun @ Pvar @ C @ D @ E @ R22 @ S ) @ ( bNF_rel_fun @ ( ( proces634752977rocess @ A ) > D ) @ ( ( proces634752977rocess @ B ) > E ) @ ( ( A > ( proces554692349s_term @ A @ Pvar ) > D > D ) > ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( B > ( proces554692349s_term @ B @ C ) > E > E ) > ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E > E > E ) > ( proces554692349s_term @ B @ C ) > E ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ D @ E @ ( proces749077512rocess @ A @ B @ R1 ) @ S ) @ ( bNF_rel_fun @ ( A > ( proces554692349s_term @ A @ Pvar ) > D > D ) @ ( B > ( proces554692349s_term @ B @ C ) > E > E ) @ ( ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E > E > E ) > ( proces554692349s_term @ B @ C ) > E ) @ ( bNF_rel_fun @ A @ B @ ( ( proces554692349s_term @ A @ Pvar ) > D > D ) @ ( ( proces554692349s_term @ B @ C ) > E > E ) @ R1 @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( D > D ) @ ( E > E ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( bNF_rel_fun @ D @ E @ D @ E @ S @ S ) ) ) @ ( bNF_rel_fun @ ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D > D > D ) @ ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E > E > E ) @ ( ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( proces554692349s_term @ B @ C ) > E ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( ( proces554692349s_term @ A @ Pvar ) > D > D > D ) @ ( ( proces554692349s_term @ B @ C ) > E > E > E ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( D > D > D ) @ ( E > E > E ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( bNF_rel_fun @ D @ E @ ( D > D ) @ ( E > E ) @ S @ ( bNF_rel_fun @ D @ E @ D @ E @ S @ S ) ) ) ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ D @ E @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ S ) ) ) ) @ ( proces2117273769s_term @ Pvar @ D @ A ) @ ( proces2117273769s_term @ C @ E @ B ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_238_process__term_Ocase__transfer,axiom,
% 3.59/1.85 ! [Pvar: $tType,D: $tType,A: $tType,B: $tType,E: $tType,C: $tType,R22: Pvar > C > $o,S: D > E > $o,R1: A > B > $o] : ( bNF_rel_fun @ ( Pvar > D ) @ ( C > E ) @ ( ( ( proces634752977rocess @ A ) > D ) > ( A > ( proces554692349s_term @ A @ Pvar ) > D ) > ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( ( proces634752977rocess @ B ) > E ) > ( B > ( proces554692349s_term @ B @ C ) > E ) > ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E ) > ( proces554692349s_term @ B @ C ) > E ) @ ( bNF_rel_fun @ Pvar @ C @ D @ E @ R22 @ S ) @ ( bNF_rel_fun @ ( ( proces634752977rocess @ A ) > D ) @ ( ( proces634752977rocess @ B ) > E ) @ ( ( A > ( proces554692349s_term @ A @ Pvar ) > D ) > ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( B > ( proces554692349s_term @ B @ C ) > E ) > ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E ) > ( proces554692349s_term @ B @ C ) > E ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ D @ E @ ( proces749077512rocess @ A @ B @ R1 ) @ S ) @ ( bNF_rel_fun @ ( A > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( B > ( proces554692349s_term @ B @ C ) > E ) @ ( ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E ) > ( proces554692349s_term @ B @ C ) > E ) @ ( bNF_rel_fun @ A @ B @ ( ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( proces554692349s_term @ B @ C ) > E ) @ R1 @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ D @ E @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ S ) ) @ ( bNF_rel_fun @ ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) > E ) @ ( ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( proces554692349s_term @ B @ C ) > E ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( ( proces554692349s_term @ A @ Pvar ) > D ) @ ( ( proces554692349s_term @ B @ C ) > E ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ D @ E @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ S ) ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ D @ E @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ S ) ) ) ) @ ( proces460752237s_term @ Pvar @ D @ A ) @ ( proces460752237s_term @ C @ E @ B ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_239_process_Ocorec__transfer,axiom,
% 3.59/1.85 ! [C: $tType,A: $tType,B: $tType,D: $tType,S: C > D > $o,R: A > B > $o] :
% 3.59/1.85 ( bNF_rel_fun @ ( C > $o ) @ ( D > $o ) @ ( ( C > A ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > B ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) )
% 3.59/1.85 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ S
% 3.59/1.85 @ ^ [Y6: $o,Z: $o] : ( Y6 = Z ) )
% 3.59/1.85 @ ( bNF_rel_fun @ ( C > A ) @ ( D > B ) @ ( ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ A @ B @ S @ R )
% 3.59/1.85 @ ( bNF_rel_fun @ ( C > $o ) @ ( D > $o ) @ ( ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) )
% 3.59/1.85 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ S
% 3.59/1.85 @ ^ [Y6: $o,Z: $o] : ( Y6 = Z ) )
% 3.59/1.85 @ ( bNF_rel_fun @ ( C > ( proces634752977rocess @ A ) ) @ ( D > ( proces634752977rocess @ B ) ) @ ( ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ S @ ( proces749077512rocess @ A @ B @ R ) )
% 3.59/1.85 @ ( bNF_rel_fun @ ( C > C ) @ ( D > D ) @ ( ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ C @ D @ S @ S )
% 3.59/1.85 @ ( bNF_rel_fun @ ( C > $o ) @ ( D > $o ) @ ( ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) )
% 3.59/1.85 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ S
% 3.59/1.85 @ ^ [Y6: $o,Z: $o] : ( Y6 = Z ) )
% 3.59/1.85 @ ( bNF_rel_fun @ ( C > ( proces634752977rocess @ A ) ) @ ( D > ( proces634752977rocess @ B ) ) @ ( ( C > C ) > ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > D ) > ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ S @ ( proces749077512rocess @ A @ B @ R ) )
% 3.59/1.85 @ ( bNF_rel_fun @ ( C > C ) @ ( D > D ) @ ( ( C > $o ) > ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > $o ) > ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ C @ D @ S @ S )
% 3.59/1.85 @ ( bNF_rel_fun @ ( C > $o ) @ ( D > $o ) @ ( ( C > ( proces634752977rocess @ A ) ) > ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > ( proces634752977rocess @ B ) ) > ( D > D ) > D > ( proces634752977rocess @ B ) )
% 3.59/1.85 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ S
% 3.59/1.85 @ ^ [Y6: $o,Z: $o] : ( Y6 = Z ) )
% 3.59/1.85 @ ( bNF_rel_fun @ ( C > ( proces634752977rocess @ A ) ) @ ( D > ( proces634752977rocess @ B ) ) @ ( ( C > C ) > C > ( proces634752977rocess @ A ) ) @ ( ( D > D ) > D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ S @ ( proces749077512rocess @ A @ B @ R ) ) @ ( bNF_rel_fun @ ( C > C ) @ ( D > D ) @ ( C > ( proces634752977rocess @ A ) ) @ ( D > ( proces634752977rocess @ B ) ) @ ( bNF_rel_fun @ C @ D @ C @ D @ S @ S ) @ ( bNF_rel_fun @ C @ D @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ S @ ( proces749077512rocess @ A @ B @ R ) ) ) ) ) ) ) ) ) ) ) )
% 3.59/1.85 @ ( proces894737309rocess @ C @ A )
% 3.59/1.85 @ ( proces894737309rocess @ D @ B ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_240_process_Odisc__transfer_I1_J,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,R: A > B > $o] :
% 3.59/1.85 ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ $o @ $o @ ( proces749077512rocess @ A @ B @ R )
% 3.59/1.85 @ ^ [Y6: $o,Z: $o] : ( Y6 = Z )
% 3.59/1.85 @ ( proces10484146Action @ A )
% 3.59/1.85 @ ( proces10484146Action @ B ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_241_process_Odisc__transfer_I2_J,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,R: A > B > $o] :
% 3.59/1.85 ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ $o @ $o @ ( proces749077512rocess @ A @ B @ R )
% 3.59/1.85 @ ^ [Y6: $o,Z: $o] : ( Y6 = Z )
% 3.59/1.85 @ ( proces401113213Choice @ A )
% 3.59/1.85 @ ( proces401113213Choice @ B ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_242_process_Octr__transfer_I2_J,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,R: A > B > $o] : ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) @ ( ( proces634752977rocess @ B ) > ( proces634752977rocess @ B ) ) @ ( proces749077512rocess @ A @ B @ R ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( proces749077512rocess @ A @ B @ R ) @ ( proces749077512rocess @ A @ B @ R ) ) @ ( proces1915862579Choice @ A ) @ ( proces1915862579Choice @ B ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_243_process_Ocase__transfer,axiom,
% 3.59/1.85 ! [A: $tType,C: $tType,D: $tType,B: $tType,R: A > B > $o,S: C > D > $o] : ( bNF_rel_fun @ ( A > ( proces634752977rocess @ A ) > C ) @ ( B > ( proces634752977rocess @ B ) > D ) @ ( ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > C ) > ( proces634752977rocess @ A ) > C ) @ ( ( ( proces634752977rocess @ B ) > ( proces634752977rocess @ B ) > D ) > ( proces634752977rocess @ B ) > D ) @ ( bNF_rel_fun @ A @ B @ ( ( proces634752977rocess @ A ) > C ) @ ( ( proces634752977rocess @ B ) > D ) @ R @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ C @ D @ ( proces749077512rocess @ A @ B @ R ) @ S ) ) @ ( bNF_rel_fun @ ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) > C ) @ ( ( proces634752977rocess @ B ) > ( proces634752977rocess @ B ) > D ) @ ( ( proces634752977rocess @ A ) > C ) @ ( ( proces634752977rocess @ B ) > D ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( ( proces634752977rocess @ A ) > C ) @ ( ( proces634752977rocess @ B ) > D ) @ ( proces749077512rocess @ A @ B @ R ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ C @ D @ ( proces749077512rocess @ A @ B @ R ) @ S ) ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ C @ D @ ( proces749077512rocess @ A @ B @ R ) @ S ) ) @ ( proces1406508781rocess @ A @ C ) @ ( proces1406508781rocess @ B @ D ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_244_process_Opred__transfer,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,R: A > B > $o] :
% 3.59/1.85 ( bNF_rel_fun @ ( A > $o ) @ ( B > $o ) @ ( ( proces634752977rocess @ A ) > $o ) @ ( ( proces634752977rocess @ B ) > $o )
% 3.59/1.85 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ R
% 3.59/1.85 @ ^ [Y6: $o,Z: $o] : ( Y6 = Z ) )
% 3.59/1.85 @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ $o @ $o @ ( proces749077512rocess @ A @ B @ R )
% 3.59/1.85 @ ^ [Y6: $o,Z: $o] : ( Y6 = Z ) )
% 3.59/1.85 @ ( proces1205983068rocess @ A )
% 3.59/1.85 @ ( proces1205983068rocess @ B ) ) ).
% 3.59/1.85
% 3.59/1.85 thf(fact_245_process_Orel__transfer,axiom,
% 3.59/1.85 ! [A: $tType,B: $tType,D: $tType,C: $tType,Sa: A > C > $o,Sc: B > D > $o] :
% 3.59/1.85 ( bNF_rel_fun @ ( A > B > $o ) @ ( C > D > $o ) @ ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ B ) > $o ) @ ( ( proces634752977rocess @ C ) > ( proces634752977rocess @ D ) > $o )
% 3.59/1.86 @ ( bNF_rel_fun @ A @ C @ ( B > $o ) @ ( D > $o ) @ Sa
% 3.59/1.86 @ ( bNF_rel_fun @ B @ D @ $o @ $o @ Sc
% 3.59/1.86 @ ^ [Y6: $o,Z: $o] : ( Y6 = Z ) ) )
% 3.59/1.86 @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ C ) @ ( ( proces634752977rocess @ B ) > $o ) @ ( ( proces634752977rocess @ D ) > $o ) @ ( proces749077512rocess @ A @ C @ Sa )
% 3.59/1.86 @ ( bNF_rel_fun @ ( proces634752977rocess @ B ) @ ( proces634752977rocess @ D ) @ $o @ $o @ ( proces749077512rocess @ B @ D @ Sc )
% 3.59/1.86 @ ^ [Y6: $o,Z: $o] : ( Y6 = Z ) ) )
% 3.59/1.86 @ ( proces749077512rocess @ A @ B )
% 3.59/1.86 @ ( proces749077512rocess @ C @ D ) ) ).
% 3.59/1.86
% 3.59/1.86 thf(fact_246_process_Octr__transfer_I1_J,axiom,
% 3.59/1.86 ! [A: $tType,B: $tType,R: A > B > $o] : ( bNF_rel_fun @ A @ B @ ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ A ) ) @ ( ( proces634752977rocess @ B ) > ( proces634752977rocess @ B ) ) @ R @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ B ) @ ( proces749077512rocess @ A @ B @ R ) @ ( proces749077512rocess @ A @ B @ R ) ) @ ( proces1525233512Action @ A ) @ ( proces1525233512Action @ B ) ) ).
% 3.59/1.86
% 3.59/1.86 thf(fact_247_process__term_Octr__transfer_I4_J,axiom,
% 3.59/1.86 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o] : ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) ) @ ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) ) @ ( proces89589571ess_CH @ A @ Pvar ) @ ( proces89589571ess_CH @ B @ C ) ) ).
% 3.59/1.86
% 3.59/1.86 thf(fact_248_process__term_Octr__transfer_I3_J,axiom,
% 3.59/1.86 ! [A: $tType,Pvar: $tType,C: $tType,B: $tType,R1: A > B > $o,R22: Pvar > C > $o] : ( bNF_rel_fun @ A @ B @ ( ( proces554692349s_term @ A @ Pvar ) > ( proces554692349s_term @ A @ Pvar ) ) @ ( ( proces554692349s_term @ B @ C ) > ( proces554692349s_term @ B @ C ) ) @ R1 @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( proces554692349s_term @ A @ Pvar ) @ ( proces554692349s_term @ B @ C ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) @ ( proces2029722208s_term @ A @ B @ Pvar @ C @ R1 @ R22 ) ) @ ( proces1454156180ss_ACT @ A @ Pvar ) @ ( proces1454156180ss_ACT @ B @ C ) ) ).
% 3.59/1.86
% 3.59/1.86 thf(fact_249_process__term_Opred__transfer,axiom,
% 3.59/1.86 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: B > D > $o] :
% 3.59/1.86 ( bNF_rel_fun @ ( A > $o ) @ ( C > $o ) @ ( ( B > $o ) > ( proces554692349s_term @ A @ B ) > $o ) @ ( ( D > $o ) > ( proces554692349s_term @ C @ D ) > $o )
% 3.59/1.86 @ ( bNF_rel_fun @ A @ C @ $o @ $o @ R1
% 3.59/1.86 @ ^ [Y6: $o,Z: $o] : ( Y6 = Z ) )
% 3.59/1.86 @ ( bNF_rel_fun @ ( B > $o ) @ ( D > $o ) @ ( ( proces554692349s_term @ A @ B ) > $o ) @ ( ( proces554692349s_term @ C @ D ) > $o )
% 3.59/1.86 @ ( bNF_rel_fun @ B @ D @ $o @ $o @ R22
% 3.59/1.86 @ ^ [Y6: $o,Z: $o] : ( Y6 = Z ) )
% 3.59/1.86 @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ B ) @ ( proces554692349s_term @ C @ D ) @ $o @ $o @ ( proces2029722208s_term @ A @ C @ B @ D @ R1 @ R22 )
% 3.59/1.86 @ ^ [Y6: $o,Z: $o] : ( Y6 = Z ) ) )
% 3.59/1.86 @ ( proces2118920028s_term @ A @ B )
% 3.59/1.86 @ ( proces2118920028s_term @ C @ D ) ) ).
% 3.59/1.86
% 3.59/1.86 thf(fact_250_process__term_Orel__transfer,axiom,
% 3.59/1.86 ! [A: $tType,C: $tType,B: $tType,D: $tType,H2: $tType,F5: $tType,G2: $tType,E: $tType,S1a: A > E > $o,S1c: C > G2 > $o,S2a: B > F5 > $o,S2c: D > H2 > $o] :
% 3.59/1.86 ( bNF_rel_fun @ ( A > C > $o ) @ ( E > G2 > $o ) @ ( ( B > D > $o ) > ( proces554692349s_term @ A @ B ) > ( proces554692349s_term @ C @ D ) > $o ) @ ( ( F5 > H2 > $o ) > ( proces554692349s_term @ E @ F5 ) > ( proces554692349s_term @ G2 @ H2 ) > $o )
% 3.59/1.86 @ ( bNF_rel_fun @ A @ E @ ( C > $o ) @ ( G2 > $o ) @ S1a
% 3.59/1.86 @ ( bNF_rel_fun @ C @ G2 @ $o @ $o @ S1c
% 3.59/1.86 @ ^ [Y6: $o,Z: $o] : ( Y6 = Z ) ) )
% 3.59/1.86 @ ( bNF_rel_fun @ ( B > D > $o ) @ ( F5 > H2 > $o ) @ ( ( proces554692349s_term @ A @ B ) > ( proces554692349s_term @ C @ D ) > $o ) @ ( ( proces554692349s_term @ E @ F5 ) > ( proces554692349s_term @ G2 @ H2 ) > $o )
% 3.59/1.86 @ ( bNF_rel_fun @ B @ F5 @ ( D > $o ) @ ( H2 > $o ) @ S2a
% 3.59/1.86 @ ( bNF_rel_fun @ D @ H2 @ $o @ $o @ S2c
% 3.59/1.86 @ ^ [Y6: $o,Z: $o] : ( Y6 = Z ) ) )
% 3.59/1.86 @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ B ) @ ( proces554692349s_term @ E @ F5 ) @ ( ( proces554692349s_term @ C @ D ) > $o ) @ ( ( proces554692349s_term @ G2 @ H2 ) > $o ) @ ( proces2029722208s_term @ A @ E @ B @ F5 @ S1a @ S2a )
% 3.59/1.86 @ ( bNF_rel_fun @ ( proces554692349s_term @ C @ D ) @ ( proces554692349s_term @ G2 @ H2 ) @ $o @ $o @ ( proces2029722208s_term @ C @ G2 @ D @ H2 @ S1c @ S2c )
% 3.59/1.86 @ ^ [Y6: $o,Z: $o] : ( Y6 = Z ) ) ) )
% 3.59/1.86 @ ( proces2029722208s_term @ A @ C @ B @ D )
% 3.59/1.86 @ ( proces2029722208s_term @ E @ G2 @ F5 @ H2 ) ) ).
% 3.59/1.86
% 3.59/1.86 thf(fact_251_process__term_Omap__transfer,axiom,
% 3.59/1.86 ! [A: $tType,C: $tType,B: $tType,D: $tType,L: $tType,J: $tType,K: $tType,I: $tType,R1b: A > I > $o,S1d: C > K > $o,R2b: B > J > $o,S2d: D > L > $o] : ( bNF_rel_fun @ ( A > C ) @ ( I > K ) @ ( ( B > D ) > ( proces554692349s_term @ A @ B ) > ( proces554692349s_term @ C @ D ) ) @ ( ( J > L ) > ( proces554692349s_term @ I @ J ) > ( proces554692349s_term @ K @ L ) ) @ ( bNF_rel_fun @ A @ I @ C @ K @ R1b @ S1d ) @ ( bNF_rel_fun @ ( B > D ) @ ( J > L ) @ ( ( proces554692349s_term @ A @ B ) > ( proces554692349s_term @ C @ D ) ) @ ( ( proces554692349s_term @ I @ J ) > ( proces554692349s_term @ K @ L ) ) @ ( bNF_rel_fun @ B @ J @ D @ L @ R2b @ S2d ) @ ( bNF_rel_fun @ ( proces554692349s_term @ A @ B ) @ ( proces554692349s_term @ I @ J ) @ ( proces554692349s_term @ C @ D ) @ ( proces554692349s_term @ K @ L ) @ ( proces2029722208s_term @ A @ I @ B @ J @ R1b @ R2b ) @ ( proces2029722208s_term @ C @ K @ D @ L @ S1d @ S2d ) ) ) @ ( proces224683037s_term @ A @ C @ B @ D ) @ ( proces224683037s_term @ I @ K @ J @ L ) ) ).
% 3.59/1.86
% 3.59/1.86 thf(fact_252_process_Omap__transfer,axiom,
% 3.59/1.86 ! [A: $tType,B: $tType,F5: $tType,E: $tType,Rb: A > E > $o,Sd: B > F5 > $o] : ( bNF_rel_fun @ ( A > B ) @ ( E > F5 ) @ ( ( proces634752977rocess @ A ) > ( proces634752977rocess @ B ) ) @ ( ( proces634752977rocess @ E ) > ( proces634752977rocess @ F5 ) ) @ ( bNF_rel_fun @ A @ E @ B @ F5 @ Rb @ Sd ) @ ( bNF_rel_fun @ ( proces634752977rocess @ A ) @ ( proces634752977rocess @ E ) @ ( proces634752977rocess @ B ) @ ( proces634752977rocess @ F5 ) @ ( proces749077512rocess @ A @ E @ Rb ) @ ( proces749077512rocess @ B @ F5 @ Sd ) ) @ ( proces370407749rocess @ A @ B ) @ ( proces370407749rocess @ E @ F5 ) ) ).
% 3.59/1.86
% 3.59/1.86 thf(fact_253_process_Omap__disc__iff_I1_J,axiom,
% 3.59/1.86 ! [B: $tType,A: $tType,F: A > B,A2: proces634752977rocess @ A] :
% 3.59/1.86 ( ( proces10484146Action @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
% 3.59/1.86 = ( proces10484146Action @ A @ A2 ) ) ).
% 3.59/1.86
% 3.59/1.86 thf(fact_254_process_Omap__disc__iff_I2_J,axiom,
% 3.59/1.86 ! [B: $tType,A: $tType,F: A > B,A2: proces634752977rocess @ A] :
% 3.59/1.86 ( ( proces401113213Choice @ B @ ( proces370407749rocess @ A @ B @ F @ A2 ) )
% 3.59/1.86 = ( proces401113213Choice @ A @ A2 ) ) ).
% 3.59/1.86
% 3.59/1.86 thf(help_If_3_1_T,axiom,
% 3.59/1.86 ! [P3: $o] :
% 3.59/1.86 ( ( P3 = $true )
% 3.59/1.86 | ( P3 = $false ) ) ).
% 3.59/1.86
% 3.59/1.86 thf(help_If_2_1_T,axiom,
% 3.59/1.86 ! [A: $tType,X7: A,Y3: A] :
% 3.59/1.86 ( ( if @ A @ $false @ X7 @ Y3 )
% 3.59/1.86 = Y3 ) ).
% 3.59/1.86
% 3.59/1.86 thf(help_If_1_1_T,axiom,
% 3.59/1.86 ! [A: $tType,X7: A,Y3: A] :
% 3.59/1.86 ( ( if @ A @ $true @ X7 @ Y3 )
% 3.59/1.86 = X7 ) ).
% 3.59/1.86
% 3.59/1.86 thf(conj_0,conjecture,
% 3.59/1.86 ( ( a3 = a2 )
% 3.59/1.86 & ( p2
% 3.59/1.86 = ( proces1652378886lution @ b @ a @ sys @ ( proces1062592052s_PROC @ a @ b @ pa ) ) ) ) ).
% 3.59/1.86 ------------------------
% 3.69/1.91 % (15727)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_15624 for (2999ds/2Mi)
% 3.69/1.91 % (15729)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_15624 for (2999ds/18Mi)
% 3.69/1.91 % (15726)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_15624 for (2999ds/2Mi)
% 3.69/1.91 % (15725)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_15624 for (2999ds/27Mi)
% 3.69/1.91 % (15724)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_15624 for (2999ds/4Mi)
% 3.69/1.91 % (15728)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_15624 for (2999ds/275Mi)
% 3.69/1.91 % (15727)Instruction limit reached!
% 3.69/1.91 % (15727)------------------------------
% 3.69/1.91 % (15727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.69/1.91 % (15727)Termination reason: Unknown
% 3.69/1.91 % (15727)Termination phase: shuffling
% 3.69/1.91
% 3.69/1.91 % (15727)Memory used [KB]: 1535
% 3.69/1.91 % (15727)Time elapsed: 0.003 s
% 3.69/1.91 % (15727)Instructions burned: 2 (million)
% 3.69/1.91 % (15727)------------------------------
% 3.69/1.91 % (15727)------------------------------
% 3.69/1.91 % (15723)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_15624 for (2999ds/183Mi)
% 3.69/1.91 % (15726)Instruction limit reached!
% 3.69/1.91 % (15726)------------------------------
% 3.69/1.91 % (15726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.69/1.91 % (15726)Termination reason: Unknown
% 3.69/1.91 % (15726)Termination phase: shuffling
% 3.69/1.91
% 3.69/1.91 % (15726)Memory used [KB]: 1663
% 3.69/1.91 % (15726)Time elapsed: 0.004 s
% 3.69/1.91 % (15726)Instructions burned: 3 (million)
% 3.69/1.91 % (15726)------------------------------
% 3.69/1.91 % (15726)------------------------------
% 3.69/1.91 % (15724)Instruction limit reached!
% 3.69/1.91 % (15724)------------------------------
% 3.69/1.91 % (15724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.69/1.91 % (15724)Termination reason: Unknown
% 3.69/1.91 % (15724)Termination phase: shuffling
% 3.69/1.91
% 3.69/1.91 % (15724)Memory used [KB]: 1663
% 3.69/1.91 % (15724)Time elapsed: 0.004 s
% 3.69/1.91 % (15724)Instructions burned: 5 (million)
% 3.69/1.91 % (15724)------------------------------
% 3.69/1.91 % (15724)------------------------------
% 3.69/1.92 % (15729)Instruction limit reached!
% 3.69/1.92 % (15729)------------------------------
% 3.69/1.92 % (15729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.69/1.92 % (15729)Termination reason: Unknown
% 3.69/1.92 % (15729)Termination phase: shuffling
% 3.69/1.92
% 3.69/1.92 % (15729)Memory used [KB]: 1918
% 3.69/1.92 % (15729)Time elapsed: 0.011 s
% 3.69/1.92 % (15729)Instructions burned: 19 (million)
% 3.69/1.92 % (15729)------------------------------
% 3.69/1.92 % (15729)------------------------------
% 3.69/1.92 % (15725)Instruction limit reached!
% 3.69/1.92 % (15725)------------------------------
% 3.69/1.92 % (15725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.69/1.92 % (15725)Termination reason: Unknown
% 3.69/1.92 % (15725)Termination phase: shuffling
% 3.69/1.92
% 3.69/1.92 % (15725)Memory used [KB]: 2174
% 3.69/1.92 % (15725)Time elapsed: 0.016 s
% 3.69/1.92 % (15725)Instructions burned: 28 (million)
% 3.69/1.92 % (15725)------------------------------
% 3.69/1.92 % (15725)------------------------------
% 3.69/1.93 % (15730)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_15624 for (2999ds/3Mi)
% 3.69/1.93 % (15731)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_15624 for (2999ds/37Mi)
% 3.69/1.93 % (15732)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_15624 for (2999ds/15Mi)
% 3.69/1.93 % (15730)Instruction limit reached!
% 3.69/1.93 % (15730)------------------------------
% 3.69/1.93 % (15730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.69/1.93 % (15730)Termination reason: Unknown
% 3.69/1.93 % (15730)Termination phase: shuffling
% 3.69/1.93
% 3.69/1.93 % (15730)Memory used [KB]: 1791
% 3.69/1.93 % (15730)Time elapsed: 0.004 s
% 3.69/1.93 % (15730)Instructions burned: 5 (million)
% 3.69/1.93 % (15730)------------------------------
% 3.69/1.93 % (15730)------------------------------
% 3.69/1.93 % (15733)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_15624 for (2999ds/3Mi)
% 3.69/1.94 % (15732)Instruction limit reached!
% 3.69/1.94 % (15732)------------------------------
% 3.69/1.94 % (15732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.69/1.94 % (15732)Termination reason: Unknown
% 3.69/1.94 % (15732)Termination phase: shuffling
% 3.69/1.94
% 3.69/1.94 % (15732)Memory used [KB]: 1918
% 3.69/1.94 % (15732)Time elapsed: 0.009 s
% 3.69/1.94 % (15732)Instructions burned: 15 (million)
% 3.69/1.94 % (15732)------------------------------
% 3.69/1.94 % (15732)------------------------------
% 3.69/1.94 % (15733)Instruction limit reached!
% 3.69/1.94 % (15733)------------------------------
% 3.69/1.94 % (15733)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.69/1.94 % (15733)Termination reason: Unknown
% 3.69/1.94 % (15733)Termination phase: shuffling
% 3.69/1.94
% 3.69/1.94 % (15733)Memory used [KB]: 1663
% 3.69/1.94 % (15733)Time elapsed: 0.003 s
% 3.69/1.94 % (15733)Instructions burned: 3 (million)
% 3.69/1.94 % (15733)------------------------------
% 3.69/1.94 % (15733)------------------------------
% 3.69/1.94 % (15734)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_15624 for (2999ds/1041Mi)
% 3.69/1.94 % (15731)Instruction limit reached!
% 3.69/1.94 % (15731)------------------------------
% 3.69/1.94 % (15731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.69/1.94 % (15731)Termination reason: Unknown
% 3.69/1.94 % (15731)Termination phase: shuffling
% 3.69/1.94
% 3.69/1.94 % (15731)Memory used [KB]: 2302
% 3.69/1.94 % (15731)Time elapsed: 0.019 s
% 3.69/1.94 % (15731)Instructions burned: 38 (million)
% 3.69/1.94 % (15731)------------------------------
% 3.69/1.94 % (15731)------------------------------
% 3.69/1.94 % (15735)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_15624 for (2999ds/7Mi)
% 3.69/1.95 % (15735)Instruction limit reached!
% 3.69/1.95 % (15735)------------------------------
% 3.69/1.95 % (15735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.69/1.95 % (15735)Termination reason: Unknown
% 3.69/1.95 % (15735)Termination phase: shuffling
% 3.69/1.95
% 3.69/1.95 % (15735)Memory used [KB]: 1791
% 3.69/1.95 % (15735)Time elapsed: 0.005 s
% 3.69/1.95 % (15735)Instructions burned: 7 (million)
% 3.69/1.95 % (15735)------------------------------
% 3.69/1.95 % (15735)------------------------------
% 3.69/1.95 % (15736)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_15624 for (2999ds/16Mi)
% 3.69/1.95 % (15737)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_15624 for (2999ds/3Mi)
% 3.69/1.95 % (15737)Instruction limit reached!
% 3.69/1.95 % (15737)------------------------------
% 3.69/1.95 % (15737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.69/1.95 % (15737)Termination reason: Unknown
% 3.69/1.95 % (15737)Termination phase: shuffling
% 3.69/1.95
% 3.69/1.95 % (15737)Memory used [KB]: 1663
% 3.69/1.95 % (15737)Time elapsed: 0.003 s
% 3.69/1.95 % (15737)Instructions burned: 3 (million)
% 3.69/1.95 % (15737)------------------------------
% 3.69/1.95 % (15737)------------------------------
% 3.69/1.96 % (15736)Instruction limit reached!
% 3.69/1.96 % (15736)------------------------------
% 3.69/1.96 % (15736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.69/1.96 % (15736)Termination reason: Unknown
% 3.69/1.96 % (15736)Termination phase: shuffling
% 3.69/1.96
% 3.69/1.96 % (15736)Memory used [KB]: 1918
% 3.69/1.96 % (15736)Time elapsed: 0.009 s
% 3.69/1.96 % (15736)Instructions burned: 16 (million)
% 3.69/1.96 % (15736)------------------------------
% 3.69/1.96 % (15736)------------------------------
% 3.69/1.96 % (15738)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_15624 for (2999ds/3Mi)
% 3.69/1.96 % (15738)Instruction limit reached!
% 3.69/1.96 % (15738)------------------------------
% 3.69/1.96 % (15738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.69/1.96 % (15738)Termination reason: Unknown
% 3.69/1.96 % (15738)Termination phase: shuffling
% 3.69/1.96
% 3.69/1.96 % (15738)Memory used [KB]: 1663
% 3.69/1.96 % (15738)Time elapsed: 0.003 s
% 3.69/1.96 % (15738)Instructions burned: 3 (million)
% 3.69/1.96 % (15738)------------------------------
% 3.69/1.96 % (15738)------------------------------
% 3.69/1.96 % (15739)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_15624 for (2999ds/7Mi)
% 3.69/1.97 % (15739)Instruction limit reached!
% 3.69/1.97 % (15739)------------------------------
% 3.69/1.97 % (15739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.69/1.97 % (15739)Termination reason: Unknown
% 3.69/1.97 % (15739)Termination phase: shuffling
% 3.69/1.97
% 3.69/1.97 % (15739)Memory used [KB]: 1791
% 3.69/1.97 % (15739)Time elapsed: 0.005 s
% 3.69/1.97 % (15739)Instructions burned: 7 (million)
% 3.69/1.97 % (15739)------------------------------
% 3.69/1.97 % (15739)------------------------------
% 3.69/1.97 % (15740)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_15624 for (2999ds/3Mi)
% 3.69/1.97 % (15740)Instruction limit reached!
% 3.69/1.97 % (15740)------------------------------
% 3.69/1.97 % (15740)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.69/1.97 % (15740)Termination reason: Unknown
% 3.69/1.97 % (15740)Termination phase: shuffling
% 3.69/1.97
% 3.69/1.97 % (15740)Memory used [KB]: 1663
% 3.69/1.97 % (15740)Time elapsed: 0.003 s
% 3.69/1.97 % (15740)Instructions burned: 3 (million)
% 3.69/1.97 % (15740)------------------------------
% 3.69/1.97 % (15740)------------------------------
% 3.69/1.97 % (15741)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_15624 for (2999ds/4Mi)
% 3.69/1.98 % (15728)Refutation not found, incomplete strategy
% 3.69/1.98 % (15728)------------------------------
% 3.69/1.98 % (15728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.69/1.98 % (15728)Termination reason: Refutation not found, incomplete strategy
% 3.69/1.98
% 3.69/1.98
% 3.69/1.98 % (15728)Memory used [KB]: 7803
% 3.69/1.98 % (15728)Time elapsed: 0.069 s
% 3.69/1.98 % (15728)Instructions burned: 140 (million)
% 3.69/1.98 % (15728)------------------------------
% 3.69/1.98 % (15728)------------------------------
% 3.69/1.98 % (15741)Instruction limit reached!
% 3.69/1.98 % (15741)------------------------------
% 3.69/1.98 % (15741)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.69/1.98 % (15741)Termination reason: Unknown
% 3.69/1.98 % (15741)Termination phase: shuffling
% 3.69/1.98
% 3.69/1.98 % (15741)Memory used [KB]: 1663
% 3.69/1.98 % (15741)Time elapsed: 0.004 s
% 3.69/1.98 % (15741)Instructions burned: 5 (million)
% 3.69/1.98 % (15741)------------------------------
% 3.69/1.98 % (15741)------------------------------
% 3.69/1.98 % (15742)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_15624 for (2999ds/18Mi)
% 3.69/1.98 % (15743)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_15624 for (2999ds/710Mi)
% 3.69/1.99 % (15744)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_15624 for (2999ds/6Mi)
% 3.69/1.99 % (15742)Instruction limit reached!
% 3.69/1.99 % (15742)------------------------------
% 3.69/1.99 % (15742)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.69/1.99 % (15742)Termination reason: Unknown
% 3.69/1.99 % (15742)Termination phase: shuffling
% 3.69/1.99
% 3.69/1.99 % (15742)Memory used [KB]: 1918
% 3.69/1.99 % (15742)Time elapsed: 0.011 s
% 3.69/1.99 % (15742)Instructions burned: 20 (million)
% 3.69/1.99 % (15742)------------------------------
% 3.69/1.99 % (15742)------------------------------
% 3.69/1.99 % (15744)Instruction limit reached!
% 3.69/1.99 % (15744)------------------------------
% 3.69/1.99 % (15744)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.69/1.99 % (15744)Termination reason: Unknown
% 3.69/1.99 % (15744)Termination phase: shuffling
% 3.69/1.99
% 3.69/1.99 % (15744)Memory used [KB]: 1791
% 3.69/1.99 % (15744)Time elapsed: 0.005 s
% 3.69/1.99 % (15744)Instructions burned: 7 (million)
% 3.69/1.99 % (15744)------------------------------
% 3.69/1.99 % (15744)------------------------------
% 3.69/1.99 % (15745)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_15624 for (2998ds/902Mi)
% 3.69/1.99 % (15746)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_15624 for (2998ds/21Mi)
% 3.69/2.00 % (15723)Instruction limit reached!
% 3.69/2.00 % (15723)------------------------------
% 3.69/2.00 % (15723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.69/2.00 % (15723)Termination reason: Unknown
% 3.69/2.00 % (15723)Termination phase: Property scanning
% 3.69/2.00
% 3.69/2.00 % (15723)Memory used [KB]: 3837
% 3.69/2.00 % (15723)Time elapsed: 0.087 s
% 3.69/2.00 % (15723)Instructions burned: 184 (million)
% 3.69/2.00 % (15723)------------------------------
% 3.69/2.00 % (15723)------------------------------
% 3.69/2.00 % (15746)Instruction limit reached!
% 3.69/2.00 % (15746)------------------------------
% 3.69/2.00 % (15746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.69/2.00 % (15746)Termination reason: Unknown
% 3.69/2.00 % (15746)Termination phase: shuffling
% 3.69/2.00
% 3.69/2.00 % (15746)Memory used [KB]: 1918
% 3.69/2.00 % (15746)Time elapsed: 0.011 s
% 3.69/2.00 % (15746)Instructions burned: 21 (million)
% 3.69/2.00 % (15746)------------------------------
% 3.69/2.00 % (15746)------------------------------
% 3.69/2.00 % (15747)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_15624 for (2998ds/5Mi)
% 3.69/2.01 % (15747)Instruction limit reached!
% 3.69/2.01 % (15747)------------------------------
% 3.69/2.01 % (15747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.69/2.01 % (15748)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_15624 for (2998ds/6Mi)
% 3.69/2.01 % (15747)Termination reason: Unknown
% 3.69/2.01 % (15747)Termination phase: shuffling
% 3.69/2.01
% 3.69/2.01 % (15747)Memory used [KB]: 1663
% 3.69/2.01 % (15747)Time elapsed: 0.004 s
% 3.69/2.01 % (15747)Instructions burned: 5 (million)
% 3.69/2.01 % (15747)------------------------------
% 3.69/2.01 % (15747)------------------------------
% 3.69/2.01 % (15748)Instruction limit reached!
% 3.69/2.01 % (15748)------------------------------
% 3.69/2.01 % (15748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.69/2.01 % (15748)Termination reason: Unknown
% 3.69/2.01 % (15748)Termination phase: shuffling
% 3.69/2.01
% 3.69/2.01 % (15748)Memory used [KB]: 1791
% 3.69/2.01 % (15748)Time elapsed: 0.005 s
% 3.69/2.01 % (15748)Instructions burned: 7 (million)
% 3.69/2.01 % (15748)------------------------------
% 3.69/2.01 % (15748)------------------------------
% 3.69/2.01 % (15749)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_15624 for (2998ds/377Mi)
% 3.69/2.02 % (15750)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_15624 for (2998ds/779Mi)
% 3.69/2.02 % (15751)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_15624 for (2998ds/19Mi)
% 4.52/2.03 % (15752)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_15624 for (2998ds/879Mi)
% 4.52/2.03 % (15751)Instruction limit reached!
% 4.52/2.03 % (15751)------------------------------
% 4.52/2.03 % (15751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.52/2.03 % (15751)Termination reason: Unknown
% 4.52/2.03 % (15751)Termination phase: shuffling
% 4.52/2.03
% 4.52/2.03 % (15751)Memory used [KB]: 2046
% 4.52/2.03 % (15751)Time elapsed: 0.011 s
% 4.52/2.03 % (15751)Instructions burned: 20 (million)
% 4.52/2.03 % (15751)------------------------------
% 4.52/2.03 % (15751)------------------------------
% 4.52/2.05 % (15753)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_15624 for (2998ds/17Mi)
% 4.52/2.06 % (15753)Instruction limit reached!
% 4.52/2.06 % (15753)------------------------------
% 4.52/2.06 % (15753)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.52/2.06 % (15753)Termination reason: Unknown
% 4.52/2.06 % (15753)Termination phase: shuffling
% 4.52/2.06
% 4.52/2.06 % (15753)Memory used [KB]: 1918
% 4.52/2.06 % (15753)Time elapsed: 0.011 s
% 4.52/2.06 % (15753)Instructions burned: 18 (million)
% 4.52/2.06 % (15753)------------------------------
% 4.52/2.06 % (15753)------------------------------
% 4.52/2.07 % (15754)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_15624 for (2998ds/3Mi)
% 4.52/2.08 % (15754)Instruction limit reached!
% 4.52/2.08 % (15754)------------------------------
% 4.52/2.08 % (15754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.52/2.08 % (15754)Termination reason: Unknown
% 4.52/2.08 % (15754)Termination phase: shuffling
% 4.52/2.08
% 4.52/2.08 % (15754)Memory used [KB]: 1663
% 4.52/2.08 % (15754)Time elapsed: 0.004 s
% 4.52/2.08 % (15754)Instructions burned: 5 (million)
% 4.52/2.08 % (15754)------------------------------
% 4.52/2.08 % (15754)------------------------------
% 4.52/2.09 % (15755)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_15624 for (2997ds/30Mi)
% 4.52/2.11 % (15755)Instruction limit reached!
% 4.52/2.11 % (15755)------------------------------
% 4.52/2.11 % (15755)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.52/2.11 % (15755)Termination reason: Unknown
% 4.52/2.11 % (15755)Termination phase: shuffling
% 4.52/2.11
% 4.52/2.11 % (15755)Memory used [KB]: 2174
% 4.52/2.11 % (15755)Time elapsed: 0.017 s
% 4.52/2.11 % (15755)Instructions burned: 31 (million)
% 4.52/2.11 % (15755)------------------------------
% 4.52/2.11 % (15755)------------------------------
% 4.52/2.12 % (15756)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_15624 for (2997ds/127Mi)
% 4.93/2.17 % (15745)Refutation not found, incomplete strategy
% 4.93/2.17 % (15745)------------------------------
% 4.93/2.17 % (15745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.93/2.17 % (15745)Termination reason: Refutation not found, incomplete strategy
% 4.93/2.17
% 4.93/2.17
% 4.93/2.17 % (15745)Memory used [KB]: 9850
% 4.93/2.17 % (15745)Time elapsed: 0.176 s
% 4.93/2.17 % (15745)Instructions burned: 364 (million)
% 4.93/2.17 % (15745)------------------------------
% 4.93/2.17 % (15745)------------------------------
% 4.93/2.18 % (15756)Instruction limit reached!
% 4.93/2.18 % (15756)------------------------------
% 4.93/2.18 % (15756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.93/2.18 % (15756)Termination reason: Unknown
% 4.93/2.18 % (15756)Termination phase: Preprocessing 3
% 4.93/2.18
% 4.93/2.18 % (15756)Memory used [KB]: 3198
% 4.93/2.18 % (15756)Time elapsed: 0.062 s
% 4.93/2.18 % (15756)Instructions burned: 127 (million)
% 4.93/2.18 % (15756)------------------------------
% 4.93/2.18 % (15756)------------------------------
% 4.93/2.19 % (15757)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_15624 for (2996ds/100Mi)
% 4.93/2.19 % (15749)Instruction limit reached!
% 4.93/2.19 % (15749)------------------------------
% 4.93/2.19 % (15749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.93/2.19 % (15749)Termination reason: Unknown
% 4.93/2.19 % (15749)Termination phase: Saturation
% 4.93/2.19
% 4.93/2.19 % (15749)Memory used [KB]: 9210
% 4.93/2.19 % (15749)Time elapsed: 0.179 s
% 4.93/2.19 % (15749)Instructions burned: 378 (million)
% 4.93/2.19 % (15749)------------------------------
% 4.93/2.19 % (15749)------------------------------
% 5.39/2.20 % (15758)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_15624 for (2996ds/3Mi)
% 5.39/2.20 % (15758)Instruction limit reached!
% 5.39/2.20 % (15758)------------------------------
% 5.39/2.20 % (15758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.39/2.20 % (15758)Termination reason: Unknown
% 5.39/2.20 % (15758)Termination phase: shuffling
% 5.39/2.20
% 5.39/2.20 % (15758)Memory used [KB]: 1663
% 5.39/2.20 % (15758)Time elapsed: 0.004 s
% 5.39/2.20 % (15758)Instructions burned: 4 (million)
% 5.39/2.20 % (15758)------------------------------
% 5.39/2.20 % (15758)------------------------------
% 5.39/2.21 % (15759)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_15624 for (2996ds/20Mi)
% 5.39/2.22 % (15759)Instruction limit reached!
% 5.39/2.22 % (15759)------------------------------
% 5.39/2.22 % (15759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.39/2.22 % (15759)Termination reason: Unknown
% 5.39/2.22 % (15759)Termination phase: shuffling
% 5.39/2.22
% 5.39/2.22 % (15759)Memory used [KB]: 2046
% 5.39/2.22 % (15759)Time elapsed: 0.012 s
% 5.39/2.22 % (15759)Instructions burned: 22 (million)
% 5.39/2.22 % (15759)------------------------------
% 5.39/2.22 % (15759)------------------------------
% 5.39/2.22 % (15760)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_15624 for (2996ds/86Mi)
% 5.39/2.23 % (15757)Instruction limit reached!
% 5.39/2.23 % (15757)------------------------------
% 5.39/2.23 % (15757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.39/2.23 % (15757)Termination reason: Unknown
% 5.39/2.23 % (15757)Termination phase: Property scanning
% 5.39/2.23
% 5.39/2.23 % (15757)Memory used [KB]: 3070
% 5.39/2.23 % (15757)Time elapsed: 0.048 s
% 5.39/2.23 % (15757)Instructions burned: 100 (million)
% 5.39/2.23 % (15757)------------------------------
% 5.39/2.23 % (15757)------------------------------
% 5.39/2.23 % (15761)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_15624 for (2996ds/107Mi)
% 5.39/2.25 % (15762)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_15624 for (2996ds/39Mi)
% 5.39/2.26 % (15760)Instruction limit reached!
% 5.39/2.26 % (15760)------------------------------
% 5.39/2.26 % (15760)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.39/2.26 % (15760)Termination reason: Unknown
% 5.39/2.26 % (15760)Termination phase: Property scanning
% 5.39/2.26
% 5.39/2.26 % (15760)Memory used [KB]: 2942
% 5.39/2.26 % (15760)Time elapsed: 0.042 s
% 5.39/2.26 % (15760)Instructions burned: 86 (million)
% 5.39/2.26 % (15760)------------------------------
% 5.39/2.26 % (15760)------------------------------
% 5.39/2.27 % (15762)Instruction limit reached!
% 5.39/2.27 % (15762)------------------------------
% 5.39/2.27 % (15762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.39/2.27 % (15762)Termination reason: Unknown
% 5.39/2.27 % (15762)Termination phase: shuffling
% 5.39/2.27
% 5.39/2.27 % (15762)Memory used [KB]: 2302
% 5.39/2.27 % (15762)Time elapsed: 0.020 s
% 5.39/2.27 % (15762)Instructions burned: 39 (million)
% 5.39/2.27 % (15762)------------------------------
% 5.39/2.27 % (15762)------------------------------
% 5.39/2.28 % (15763)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_15624 for (2996ds/448Mi)
% 5.39/2.28 % (15764)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_15624 for (2996ds/46Mi)
% 5.39/2.28 % (15761)Instruction limit reached!
% 5.39/2.28 % (15761)------------------------------
% 5.39/2.28 % (15761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.39/2.28 % (15761)Termination reason: Unknown
% 5.39/2.28 % (15761)Termination phase: SInE selection
% 5.39/2.28
% 5.39/2.28 % (15761)Memory used [KB]: 2942
% 5.39/2.28 % (15761)Time elapsed: 0.052 s
% 5.39/2.28 % (15761)Instructions burned: 108 (million)
% 5.39/2.28 % (15761)------------------------------
% 5.39/2.28 % (15761)------------------------------
% 5.87/2.30 % (15765)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_15624 for (2995ds/98Mi)
% 5.87/2.31 % (15764)Instruction limit reached!
% 5.87/2.31 % (15764)------------------------------
% 5.87/2.31 % (15764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.87/2.31 % (15764)Termination reason: Unknown
% 5.87/2.31 % (15764)Termination phase: shuffling
% 5.87/2.31
% 5.87/2.31 % (15764)Memory used [KB]: 2302
% 5.87/2.31 % (15764)Time elapsed: 0.024 s
% 5.87/2.31 % (15764)Instructions burned: 47 (million)
% 5.87/2.31 % (15764)------------------------------
% 5.87/2.31 % (15764)------------------------------
% 5.87/2.32 % (15743)Instruction limit reached!
% 5.87/2.32 % (15743)------------------------------
% 5.87/2.32 % (15743)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.87/2.32 % (15743)Termination reason: Unknown
% 5.87/2.32 % (15743)Termination phase: Saturation
% 5.87/2.32
% 5.87/2.32 % (15743)Memory used [KB]: 8827
% 5.87/2.32 % (15743)Time elapsed: 0.359 s
% 5.87/2.32 % (15743)Instructions burned: 712 (million)
% 5.87/2.32 % (15743)------------------------------
% 5.87/2.32 % (15743)------------------------------
% 5.87/2.32 % (15766)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_15624 for (2995ds/507Mi)
% 5.87/2.34 % (15767)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_15624 for (2995ds/149Mi)
% 5.87/2.35 % (15765)Instruction limit reached!
% 5.87/2.35 % (15765)------------------------------
% 5.87/2.35 % (15765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.87/2.35 % (15765)Termination reason: Unknown
% 5.87/2.35 % (15765)Termination phase: Property scanning
% 5.87/2.35
% 5.87/2.35 % (15765)Memory used [KB]: 3070
% 5.87/2.35 % (15765)Time elapsed: 0.048 s
% 5.87/2.35 % (15765)Instructions burned: 99 (million)
% 5.87/2.35 % (15765)------------------------------
% 5.87/2.35 % (15765)------------------------------
% 5.87/2.36 % (15768)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_15624 for (2995ds/39Mi)
% 5.87/2.38 % (15750)Instruction limit reached!
% 5.87/2.38 % (15750)------------------------------
% 5.87/2.38 % (15750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.87/2.38 % (15750)Termination reason: Unknown
% 5.87/2.38 % (15750)Termination phase: Saturation
% 5.87/2.38
% 5.87/2.38 % (15750)Memory used [KB]: 9850
% 5.87/2.38 % (15750)Time elapsed: 0.361 s
% 5.87/2.38 % (15750)Instructions burned: 780 (million)
% 5.87/2.38 % (15750)------------------------------
% 5.87/2.38 % (15750)------------------------------
% 5.87/2.38 % (15768)Instruction limit reached!
% 5.87/2.38 % (15768)------------------------------
% 5.87/2.38 % (15768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.87/2.38 % (15768)Termination reason: Unknown
% 5.87/2.38 % (15768)Termination phase: shuffling
% 5.87/2.38
% 5.87/2.38 % (15768)Memory used [KB]: 2302
% 5.87/2.38 % (15768)Time elapsed: 0.021 s
% 5.87/2.38 % (15768)Instructions burned: 39 (million)
% 5.87/2.38 % (15768)------------------------------
% 5.87/2.38 % (15768)------------------------------
% 5.87/2.40 % (15769)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_15624 for (2994ds/6Mi)
% 6.50/2.40 % (15769)Instruction limit reached!
% 6.50/2.40 % (15769)------------------------------
% 6.50/2.40 % (15769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.50/2.40 % (15769)Termination reason: Unknown
% 6.50/2.40 % (15769)Termination phase: shuffling
% 6.50/2.40
% 6.50/2.40 % (15769)Memory used [KB]: 1791
% 6.50/2.40 % (15769)Time elapsed: 0.005 s
% 6.50/2.40 % (15769)Instructions burned: 6 (million)
% 6.50/2.40 % (15769)------------------------------
% 6.50/2.40 % (15769)------------------------------
% 6.50/2.40 % (15770)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_15624 for (2994ds/1087Mi)
% 6.50/2.41 % (15767)Instruction limit reached!
% 6.50/2.41 % (15767)------------------------------
% 6.50/2.41 % (15767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.50/2.41 % (15767)Termination reason: Unknown
% 6.50/2.41 % (15767)Termination phase: Property scanning
% 6.50/2.41
% 6.50/2.41 % (15767)Memory used [KB]: 3709
% 6.50/2.41 % (15767)Time elapsed: 0.072 s
% 6.50/2.41 % (15767)Instructions burned: 149 (million)
% 6.50/2.41 % (15767)------------------------------
% 6.50/2.41 % (15767)------------------------------
% 6.50/2.42 % (15771)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_15624 for (2994ds/47Mi)
% 6.50/2.42 % (15772)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_15624 for (2994ds/44Mi)
% 6.50/2.43 % (15734)Instruction limit reached!
% 6.50/2.43 % (15734)------------------------------
% 6.50/2.43 % (15734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.50/2.43 % (15734)Termination reason: Unknown
% 6.50/2.43 % (15734)Termination phase: Saturation
% 6.50/2.43
% 6.50/2.43 % (15734)Memory used [KB]: 11513
% 6.50/2.43 % (15734)Time elapsed: 0.496 s
% 6.50/2.43 % (15734)Instructions burned: 1041 (million)
% 6.50/2.43 % (15734)------------------------------
% 6.50/2.43 % (15734)------------------------------
% 6.50/2.44 % (15771)Instruction limit reached!
% 6.50/2.44 % (15771)------------------------------
% 6.50/2.44 % (15771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.50/2.44 % (15771)Termination reason: Unknown
% 6.50/2.44 % (15771)Termination phase: shuffling
% 6.50/2.44
% 6.50/2.44 % (15771)Memory used [KB]: 2302
% 6.50/2.44 % (15771)Time elapsed: 0.024 s
% 6.50/2.44 % (15771)Instructions burned: 48 (million)
% 6.50/2.44 % (15771)------------------------------
% 6.50/2.44 % (15771)------------------------------
% 6.50/2.44 % (15752)Instruction limit reached!
% 6.50/2.44 % (15752)------------------------------
% 6.50/2.44 % (15752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.50/2.44 % (15752)Termination reason: Unknown
% 6.50/2.44 % (15752)Termination phase: Saturation
% 6.50/2.44
% 6.50/2.44 % (15752)Memory used [KB]: 8699
% 6.50/2.44 % (15752)Time elapsed: 0.420 s
% 6.50/2.44 % (15752)Instructions burned: 879 (million)
% 6.50/2.44 % (15752)------------------------------
% 6.50/2.44 % (15752)------------------------------
% 6.50/2.45 % (15772)Instruction limit reached!
% 6.50/2.45 % (15772)------------------------------
% 6.50/2.45 % (15772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.50/2.45 % (15772)Termination reason: Unknown
% 6.50/2.45 % (15772)Termination phase: shuffling
% 6.50/2.45
% 6.50/2.45 % (15772)Memory used [KB]: 2430
% 6.50/2.45 % (15772)Time elapsed: 0.023 s
% 6.50/2.45 % (15772)Instructions burned: 45 (million)
% 6.50/2.45 % (15772)------------------------------
% 6.50/2.45 % (15772)------------------------------
% 6.50/2.45 % (15773)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_15624 for (2994ds/432Mi)
% 6.50/2.45 % (15774)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_15624 for (2994ds/62Mi)
% 6.50/2.46 % (15775)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_15624 for (2994ds/31Mi)
% 6.50/2.46 % (15776)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_15624 for (2994ds/96Mi)
% 6.50/2.48 % (15775)Instruction limit reached!
% 6.50/2.48 % (15775)------------------------------
% 6.50/2.48 % (15775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.50/2.48 % (15775)Termination reason: Unknown
% 6.50/2.48 % (15775)Termination phase: shuffling
% 6.50/2.48
% 6.50/2.48 % (15775)Memory used [KB]: 2046
% 6.50/2.48 % (15775)Time elapsed: 0.016 s
% 6.50/2.48 % (15775)Instructions burned: 31 (million)
% 6.50/2.48 % (15775)------------------------------
% 6.50/2.48 % (15775)------------------------------
% 6.50/2.48 % (15763)Instruction limit reached!
% 6.50/2.48 % (15763)------------------------------
% 6.50/2.48 % (15763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.50/2.48 % (15763)Termination reason: Unknown
% 6.50/2.48 % (15763)Termination phase: Saturation
% 6.50/2.48
% 6.50/2.48 % (15763)Memory used [KB]: 9210
% 6.50/2.48 % (15763)Time elapsed: 0.206 s
% 6.50/2.48 % (15763)Instructions burned: 449 (million)
% 6.50/2.48 % (15763)------------------------------
% 6.50/2.48 % (15763)------------------------------
% 6.50/2.48 % (15774)Instruction limit reached!
% 6.50/2.48 % (15774)------------------------------
% 6.50/2.48 % (15774)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.50/2.48 % (15774)Termination reason: Unknown
% 6.50/2.48 % (15774)Termination phase: shuffling
% 6.50/2.48
% 6.50/2.48 % (15774)Memory used [KB]: 2814
% 6.50/2.48 % (15774)Time elapsed: 0.031 s
% 6.50/2.48 % (15774)Instructions burned: 63 (million)
% 6.50/2.48 % (15774)------------------------------
% 6.50/2.48 % (15774)------------------------------
% 6.50/2.49 % (15777)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_15624 for (2993ds/453Mi)
% 7.47/2.50 % (15778)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_15624 for (2993ds/71Mi)
% 7.47/2.50 % (15779)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_15624 for (2993ds/83Mi)
% 7.47/2.51 % (15776)Instruction limit reached!
% 7.47/2.51 % (15776)------------------------------
% 7.47/2.51 % (15776)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.51 % (15776)Termination reason: Unknown
% 7.47/2.51 % (15776)Termination phase: Property scanning
% 7.47/2.51
% 7.47/2.51 % (15776)Memory used [KB]: 2942
% 7.47/2.51 % (15776)Time elapsed: 0.047 s
% 7.47/2.51 % (15776)Instructions burned: 97 (million)
% 7.47/2.51 % (15776)------------------------------
% 7.47/2.51 % (15776)------------------------------
% 7.47/2.52 % (15766)Refutation not found, incomplete strategy
% 7.47/2.52 % (15766)------------------------------
% 7.47/2.52 % (15766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.52 % (15766)Termination reason: Refutation not found, incomplete strategy
% 7.47/2.52
% 7.47/2.52
% 7.47/2.52 % (15766)Memory used [KB]: 10490
% 7.47/2.52 % (15766)Time elapsed: 0.201 s
% 7.47/2.52 % (15766)Instructions burned: 415 (million)
% 7.47/2.52 % (15766)------------------------------
% 7.47/2.52 % (15766)------------------------------
% 7.47/2.52 % (15780)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_15624 for (2993ds/11Mi)
% 7.47/2.53 % (15780)Instruction limit reached!
% 7.47/2.53 % (15780)------------------------------
% 7.47/2.53 % (15780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.53 % (15780)Termination reason: Unknown
% 7.47/2.53 % (15780)Termination phase: shuffling
% 7.47/2.53
% 7.47/2.53 % (15780)Memory used [KB]: 1791
% 7.47/2.53 % (15780)Time elapsed: 0.007 s
% 7.47/2.53 % (15780)Instructions burned: 11 (million)
% 7.47/2.53 % (15780)------------------------------
% 7.47/2.53 % (15780)------------------------------
% 7.47/2.53 % (15778)Instruction limit reached!
% 7.47/2.53 % (15778)------------------------------
% 7.47/2.53 % (15778)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.53 % (15778)Termination reason: Unknown
% 7.47/2.53 % (15778)Termination phase: shuffling
% 7.47/2.53
% 7.47/2.53 % (15778)Memory used [KB]: 2814
% 7.47/2.53 % (15778)Time elapsed: 0.036 s
% 7.47/2.53 % (15778)Instructions burned: 72 (million)
% 7.47/2.53 % (15778)------------------------------
% 7.47/2.53 % (15778)------------------------------
% 7.47/2.54 % (15781)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_15624 for (2993ds/41Mi)
% 7.47/2.54 % (15779)Instruction limit reached!
% 7.47/2.54 % (15779)------------------------------
% 7.47/2.54 % (15779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.54 % (15779)Termination reason: Unknown
% 7.47/2.54 % (15779)Termination phase: Property scanning
% 7.47/2.54
% 7.47/2.54 % (15779)Memory used [KB]: 2942
% 7.47/2.54 % (15779)Time elapsed: 0.041 s
% 7.47/2.54 % (15779)Instructions burned: 83 (million)
% 7.47/2.54 % (15779)------------------------------
% 7.47/2.54 % (15779)------------------------------
% 7.47/2.55 % (15782)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_15624 for (2993ds/6Mi)
% 7.47/2.55 % (15783)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_15624 for (2993ds/150Mi)
% 7.47/2.55 % (15782)Instruction limit reached!
% 7.47/2.55 % (15782)------------------------------
% 7.47/2.55 % (15782)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.55 % (15782)Termination reason: Unknown
% 7.47/2.55 % (15782)Termination phase: shuffling
% 7.47/2.55
% 7.47/2.55 % (15782)Memory used [KB]: 1791
% 7.47/2.55 % (15782)Time elapsed: 0.005 s
% 7.47/2.55 % (15782)Instructions burned: 7 (million)
% 7.47/2.55 % (15782)------------------------------
% 7.47/2.55 % (15782)------------------------------
% 7.47/2.56 % (15784)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_15624 for (2993ds/343Mi)
% 7.47/2.56 % (15781)Instruction limit reached!
% 7.47/2.56 % (15781)------------------------------
% 7.47/2.56 % (15781)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.56 % (15781)Termination reason: Unknown
% 7.47/2.56 % (15781)Termination phase: shuffling
% 7.47/2.56
% 7.47/2.56 % (15781)Memory used [KB]: 2430
% 7.47/2.56 % (15781)Time elapsed: 0.021 s
% 7.47/2.56 % (15781)Instructions burned: 41 (million)
% 7.47/2.56 % (15781)------------------------------
% 7.47/2.56 % (15781)------------------------------
% 7.47/2.56 % (15785)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_15624 for (2993ds/109Mi)
% 7.47/2.57 % (15786)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_15624 for (2993ds/253Mi)
% 7.93/2.62 % (15785)Instruction limit reached!
% 7.93/2.62 % (15785)------------------------------
% 7.93/2.62 % (15785)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.93/2.62 % (15785)Termination reason: Unknown
% 7.93/2.62 % (15785)Termination phase: SInE selection
% 7.93/2.62
% 7.93/2.62 % (15785)Memory used [KB]: 2942
% 7.93/2.62 % (15785)Time elapsed: 0.053 s
% 7.93/2.62 % (15785)Instructions burned: 111 (million)
% 7.93/2.62 % (15785)------------------------------
% 7.93/2.62 % (15785)------------------------------
% 7.93/2.62 % (15783)Instruction limit reached!
% 7.93/2.62 % (15783)------------------------------
% 7.93/2.62 % (15783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.93/2.62 % (15783)Termination reason: Unknown
% 7.93/2.62 % (15783)Termination phase: Preprocessing 3
% 7.93/2.62
% 7.93/2.62 % (15783)Memory used [KB]: 3582
% 7.93/2.62 % (15783)Time elapsed: 0.072 s
% 7.93/2.62 % (15783)Instructions burned: 150 (million)
% 7.93/2.62 % (15783)------------------------------
% 7.93/2.62 % (15783)------------------------------
% 7.93/2.63 % (15787)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_15624 for (2992ds/140Mi)
% 7.93/2.63 % (15788)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_15624 for (2992ds/614Mi)
% 7.93/2.65 % (15773)Instruction limit reached!
% 7.93/2.65 % (15773)------------------------------
% 7.93/2.65 % (15773)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.93/2.65 % (15773)Termination reason: Unknown
% 7.93/2.65 % (15773)Termination phase: Saturation
% 7.93/2.65
% 7.93/2.65 % (15773)Memory used [KB]: 4605
% 7.93/2.65 % (15773)Time elapsed: 0.205 s
% 7.93/2.65 % (15773)Instructions burned: 432 (million)
% 7.93/2.65 % (15773)------------------------------
% 7.93/2.65 % (15773)------------------------------
% 7.93/2.67 % (15789)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_15624 for (2992ds/202Mi)
% 7.93/2.69 % (15786)Instruction limit reached!
% 7.93/2.69 % (15786)------------------------------
% 7.93/2.69 % (15786)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.93/2.69 % (15786)Termination reason: Unknown
% 7.93/2.69 % (15786)Termination phase: Saturation
% 7.93/2.69
% 7.93/2.70 % (15786)Memory used [KB]: 4605
% 7.93/2.70 % (15786)Time elapsed: 0.122 s
% 7.93/2.70 % (15786)Instructions burned: 253 (million)
% 7.93/2.70 % (15786)------------------------------
% 7.93/2.70 % (15786)------------------------------
% 8.44/2.70 % (15777)Instruction limit reached!
% 8.44/2.70 % (15777)------------------------------
% 8.44/2.70 % (15777)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.44/2.70 % (15777)Termination reason: Unknown
% 8.44/2.70 % (15777)Termination phase: Saturation
% 8.44/2.70
% 8.44/2.70 % (15777)Memory used [KB]: 9210
% 8.44/2.70 % (15777)Time elapsed: 0.207 s
% 8.44/2.70 % (15777)Instructions burned: 453 (million)
% 8.44/2.70 % (15777)------------------------------
% 8.44/2.70 % (15777)------------------------------
% 8.44/2.70 % (15787)Instruction limit reached!
% 8.44/2.70 % (15787)------------------------------
% 8.44/2.70 % (15787)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.44/2.70 % (15787)Termination reason: Unknown
% 8.44/2.70 % (15787)Termination phase: Saturation
% 8.44/2.70
% 8.44/2.70 % (15787)Memory used [KB]: 7803
% 8.44/2.70 % (15787)Time elapsed: 0.070 s
% 8.44/2.70 % (15787)Instructions burned: 141 (million)
% 8.44/2.70 % (15787)------------------------------
% 8.44/2.70 % (15787)------------------------------
% 8.44/2.71 % (15790)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_15624 for (2991ds/339Mi)
% 8.44/2.71 % (15791)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_15624 for (2991ds/283Mi)
% 8.44/2.71 % (15784)Instruction limit reached!
% 8.44/2.71 % (15784)------------------------------
% 8.44/2.71 % (15784)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.44/2.71 % (15784)Termination reason: Unknown
% 8.44/2.71 % (15784)Termination phase: Saturation
% 8.44/2.71
% 8.44/2.71 % (15784)Memory used [KB]: 8827
% 8.44/2.71 % (15784)Time elapsed: 0.161 s
% 8.44/2.71 % (15784)Instructions burned: 345 (million)
% 8.44/2.71 % (15784)------------------------------
% 8.44/2.71 % (15784)------------------------------
% 8.44/2.72 % (15792)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_15624 for (2991ds/134Mi)
% 8.44/2.73 % (15793)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_15624 for (2991ds/298Mi)
% 8.44/2.74 % (15789)Refutation not found, incomplete strategy
% 8.44/2.74 % (15789)------------------------------
% 8.44/2.74 % (15789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.44/2.74 % (15789)Termination reason: Refutation not found, incomplete strategy
% 8.44/2.74
% 8.44/2.74
% 8.44/2.74 % (15789)Memory used [KB]: 7803
% 8.44/2.74 % (15789)Time elapsed: 0.070 s
% 8.44/2.74 % (15789)Instructions burned: 143 (million)
% 8.44/2.74 % (15789)------------------------------
% 8.44/2.74 % (15789)------------------------------
% 8.44/2.76 % (15794)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_15624 for (2991ds/192Mi)
% 8.44/2.78 % (15792)Instruction limit reached!
% 8.44/2.78 % (15792)------------------------------
% 8.44/2.78 % (15792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.44/2.78 % (15792)Termination reason: Unknown
% 8.44/2.78 % (15792)Termination phase: Preprocessing 3
% 8.44/2.78
% 8.44/2.78 % (15792)Memory used [KB]: 3454
% 8.44/2.78 % (15792)Time elapsed: 0.065 s
% 8.44/2.78 % (15792)Instructions burned: 135 (million)
% 8.44/2.78 % (15792)------------------------------
% 8.44/2.78 % (15792)------------------------------
% 9.09/2.80 % (15795)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_15624 for (2990ds/258Mi)
% 9.09/2.84 % (15791)Instruction limit reached!
% 9.09/2.84 % (15791)------------------------------
% 9.09/2.84 % (15791)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.09/2.84 % (15791)Termination reason: Unknown
% 9.09/2.84 % (15791)Termination phase: Property scanning
% 9.09/2.84
% 9.09/2.84 % (15791)Memory used [KB]: 4093
% 9.09/2.84 % (15791)Time elapsed: 0.130 s
% 9.09/2.84 % (15791)Instructions burned: 283 (million)
% 9.09/2.84 % (15791)------------------------------
% 9.09/2.84 % (15791)------------------------------
% 9.09/2.85 % (15794)Instruction limit reached!
% 9.09/2.85 % (15794)------------------------------
% 9.09/2.85 % (15794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.09/2.85 % (15794)Termination reason: Unknown
% 9.09/2.85 % (15794)Termination phase: Function definition elimination
% 9.09/2.85
% 9.09/2.85 % (15794)Memory used [KB]: 3837
% 9.09/2.85 % (15794)Time elapsed: 0.092 s
% 9.09/2.85 % (15794)Instructions burned: 193 (million)
% 9.09/2.85 % (15794)------------------------------
% 9.09/2.85 % (15794)------------------------------
% 9.09/2.86 % (15796)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_15624 for (2990ds/90Mi)
% 9.09/2.86 % (15797)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_15624 for (2990ds/231Mi)
% 9.09/2.87 % (15793)Instruction limit reached!
% 9.09/2.87 % (15793)------------------------------
% 9.09/2.87 % (15793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.09/2.87 % (15793)Termination reason: Unknown
% 9.09/2.87 % (15793)Termination phase: Saturation
% 9.09/2.87
% 9.09/2.87 % (15793)Memory used [KB]: 8571
% 9.09/2.87 % (15793)Time elapsed: 0.137 s
% 9.09/2.87 % (15793)Instructions burned: 300 (million)
% 9.09/2.87 % (15793)------------------------------
% 9.09/2.87 % (15793)------------------------------
% 9.09/2.87 % (15790)Instruction limit reached!
% 9.09/2.87 % (15790)------------------------------
% 9.09/2.87 % (15790)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.09/2.87 % (15790)Termination reason: Unknown
% 9.09/2.87 % (15790)Termination phase: Saturation
% 9.09/2.87
% 9.09/2.87 % (15790)Memory used [KB]: 8187
% 9.09/2.87 % (15790)Time elapsed: 0.159 s
% 9.09/2.87 % (15790)Instructions burned: 341 (million)
% 9.09/2.87 % (15790)------------------------------
% 9.09/2.87 % (15790)------------------------------
% 9.09/2.88 % (15798)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_15624 for (2990ds/458Mi)
% 9.09/2.89 % (15799)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_15624 for (2990ds/31Mi)
% 9.67/2.90 % (15799)Instruction limit reached!
% 9.67/2.90 % (15799)------------------------------
% 9.67/2.90 % (15799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.67/2.90 % (15799)Termination reason: Unknown
% 9.67/2.90 % (15799)Termination phase: shuffling
% 9.67/2.90
% 9.67/2.90 % (15799)Memory used [KB]: 2174
% 9.67/2.90 % (15799)Time elapsed: 0.016 s
% 9.67/2.90 % (15799)Instructions burned: 31 (million)
% 9.67/2.90 % (15799)------------------------------
% 9.67/2.90 % (15799)------------------------------
% 9.67/2.90 % (15796)Instruction limit reached!
% 9.67/2.90 % (15796)------------------------------
% 9.67/2.90 % (15796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.67/2.90 % (15796)Termination reason: Unknown
% 9.67/2.90 % (15796)Termination phase: Property scanning
% 9.67/2.90
% 9.67/2.90 % (15796)Memory used [KB]: 2942
% 9.67/2.90 % (15796)Time elapsed: 0.046 s
% 9.67/2.90 % (15796)Instructions burned: 92 (million)
% 9.67/2.90 % (15796)------------------------------
% 9.67/2.90 % (15796)------------------------------
% 9.67/2.91 % (15795)Instruction limit reached!
% 9.67/2.91 % (15795)------------------------------
% 9.67/2.91 % (15795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.67/2.91 % (15795)Termination reason: Unknown
% 9.67/2.91 % (15795)Termination phase: Property scanning
% 9.67/2.91
% 9.67/2.91 % (15795)Memory used [KB]: 3326
% 9.67/2.91 % (15795)Time elapsed: 0.117 s
% 9.67/2.91 % (15795)Instructions burned: 258 (million)
% 9.67/2.91 % (15795)------------------------------
% 9.67/2.91 % (15795)------------------------------
% 9.67/2.92 % (15800)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_15624 for (2989ds/297Mi)
% 9.67/2.92 % (15801)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_15624 for (2989ds/987Mi)
% 9.67/2.92 % (15770)Instruction limit reached!
% 9.67/2.92 % (15770)------------------------------
% 9.67/2.92 % (15770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.67/2.92 % (15770)Termination reason: Unknown
% 9.67/2.92 % (15770)Termination phase: Saturation
% 9.67/2.92
% 9.67/2.92 % (15770)Memory used [KB]: 9210
% 9.67/2.92 % (15770)Time elapsed: 0.523 s
% 9.67/2.92 % (15770)Instructions burned: 1088 (million)
% 9.67/2.92 % (15770)------------------------------
% 9.67/2.92 % (15770)------------------------------
% 9.67/2.92 % (15788)Instruction limit reached!
% 9.67/2.92 % (15788)------------------------------
% 9.67/2.92 % (15788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.67/2.92 % (15788)Termination reason: Unknown
% 9.67/2.92 % (15788)Termination phase: Saturation
% 9.67/2.92
% 9.67/2.92 % (15788)Memory used [KB]: 9850
% 9.67/2.92 % (15788)Time elapsed: 0.291 s
% 9.67/2.92 % (15788)Instructions burned: 614 (million)
% 9.67/2.92 % (15788)------------------------------
% 9.67/2.92 % (15788)------------------------------
% 9.67/2.93 % (15802)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_15624 for (2989ds/182Mi)
% 9.67/2.94 % (15803)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_15624 for (2989ds/182Mi)
% 9.67/2.94 % (15804)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_15624 for (2989ds/154Mi)
% 9.67/2.97 % (15797)Instruction limit reached!
% 9.67/2.97 % (15797)------------------------------
% 9.67/2.97 % (15797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.67/2.97 % (15797)Termination reason: Unknown
% 9.67/2.97 % (15797)Termination phase: Property scanning
% 9.67/2.97
% 9.67/2.97 % (15797)Memory used [KB]: 4093
% 9.67/2.97 % (15797)Time elapsed: 0.108 s
% 9.67/2.97 % (15797)Instructions burned: 232 (million)
% 9.67/2.97 % (15797)------------------------------
% 9.67/2.97 % (15797)------------------------------
% 9.67/2.99 % (15805)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_15624 for (2989ds/79Mi)
% 9.67/3.01 % (15804)Instruction limit reached!
% 9.67/3.01 % (15804)------------------------------
% 9.67/3.01 % (15804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.67/3.01 % (15804)Termination reason: Unknown
% 9.67/3.01 % (15804)Termination phase: Preprocessing 1
% 9.67/3.01
% 9.67/3.01 % (15804)Memory used [KB]: 3326
% 9.67/3.01 % (15804)Time elapsed: 0.072 s
% 9.67/3.01 % (15804)Instructions burned: 154 (million)
% 9.67/3.01 % (15804)------------------------------
% 9.67/3.01 % (15804)------------------------------
% 9.67/3.01 % (15802)Instruction limit reached!
% 9.67/3.01 % (15802)------------------------------
% 9.67/3.01 % (15802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.67/3.01 % (15802)Termination reason: Unknown
% 9.67/3.01 % (15802)Termination phase: Property scanning
% 9.67/3.01
% 9.67/3.01 % (15802)Memory used [KB]: 3709
% 9.67/3.01 % (15802)Time elapsed: 0.086 s
% 9.67/3.01 % (15802)Instructions burned: 183 (million)
% 9.67/3.01 % (15802)------------------------------
% 9.67/3.01 % (15802)------------------------------
% 9.67/3.02 % (15803)Instruction limit reached!
% 9.67/3.02 % (15803)------------------------------
% 9.67/3.02 % (15803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.67/3.02 % (15803)Termination reason: Unknown
% 9.67/3.02 % (15803)Termination phase: Property scanning
% 9.67/3.02
% 9.67/3.02 % (15803)Memory used [KB]: 3837
% 9.67/3.02 % (15803)Time elapsed: 0.087 s
% 9.67/3.02 % (15803)Instructions burned: 183 (million)
% 9.67/3.02 % (15803)------------------------------
% 9.67/3.02 % (15803)------------------------------
% 9.67/3.02 % (15805)Instruction limit reached!
% 9.67/3.02 % (15805)------------------------------
% 9.67/3.02 % (15805)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.67/3.02 % (15805)Termination reason: Unknown
% 9.67/3.02 % (15805)Termination phase: shuffling
% 9.67/3.02
% 9.67/3.02 % (15805)Memory used [KB]: 2942
% 9.67/3.02 % (15805)Time elapsed: 0.040 s
% 9.67/3.02 % (15805)Instructions burned: 79 (million)
% 9.67/3.02 % (15805)------------------------------
% 9.67/3.02 % (15805)------------------------------
% 11.46/3.03 % (15806)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_15624 for (2988ds/216Mi)
% 11.46/3.03 % (15807)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_15624 for (2988ds/114Mi)
% 11.46/3.04 % (15808)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_15624 for (2988ds/922Mi)
% 11.46/3.04 % (15809)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_15624 for (2988ds/182Mi)
% 11.46/3.05 % (15800)Instruction limit reached!
% 11.46/3.05 % (15800)------------------------------
% 11.46/3.05 % (15800)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.46/3.05 % (15800)Termination reason: Unknown
% 11.46/3.05 % (15800)Termination phase: Saturation
% 11.46/3.05
% 11.46/3.05 % (15800)Memory used [KB]: 8699
% 11.46/3.05 % (15800)Time elapsed: 0.140 s
% 11.46/3.05 % (15800)Instructions burned: 298 (million)
% 11.46/3.05 % (15800)------------------------------
% 11.46/3.05 % (15800)------------------------------
% 11.46/3.07 % (15810)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_15624 for (2988ds/164Mi)
% 11.46/3.08 % (15807)Instruction limit reached!
% 11.46/3.08 % (15807)------------------------------
% 11.46/3.08 % (15807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.46/3.08 % (15807)Termination reason: Unknown
% 11.46/3.08 % (15807)Termination phase: Naming
% 11.46/3.08
% 11.46/3.08 % (15807)Memory used [KB]: 3326
% 11.46/3.08 % (15807)Time elapsed: 0.056 s
% 11.46/3.08 % (15807)Instructions burned: 115 (million)
% 11.46/3.08 % (15807)------------------------------
% 11.46/3.08 % (15807)------------------------------
% 11.46/3.10 % (15798)Instruction limit reached!
% 11.46/3.10 % (15798)------------------------------
% 11.46/3.10 % (15798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.46/3.10 % (15798)Termination reason: Unknown
% 11.46/3.10 % (15798)Termination phase: Saturation
% 11.46/3.10
% 11.46/3.10 % (15798)Memory used [KB]: 9210
% 11.46/3.10 % (15798)Time elapsed: 0.216 s
% 11.46/3.10 % (15798)Instructions burned: 458 (million)
% 11.46/3.10 % (15798)------------------------------
% 11.46/3.10 % (15798)------------------------------
% 11.46/3.10 % (15811)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_15624 for (2987ds/50Mi)
% 11.46/3.11 % (15812)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_15624 for (2987ds/368Mi)
% 11.46/3.12 % (15811)Instruction limit reached!
% 11.46/3.12 % (15811)------------------------------
% 11.46/3.12 % (15811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.46/3.12 % (15811)Termination reason: Unknown
% 11.46/3.12 % (15811)Termination phase: shuffling
% 11.46/3.12
% 11.46/3.12 % (15811)Memory used [KB]: 2430
% 11.46/3.12 % (15811)Time elapsed: 0.025 s
% 11.46/3.12 % (15811)Instructions burned: 50 (million)
% 11.46/3.12 % (15811)------------------------------
% 11.46/3.12 % (15811)------------------------------
% 11.46/3.13 % (15806)Instruction limit reached!
% 11.46/3.13 % (15806)------------------------------
% 11.46/3.13 % (15806)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.46/3.13 % (15806)Termination reason: Unknown
% 11.46/3.13 % (15806)Termination phase: Preprocessing 3
% 11.46/3.13
% 11.46/3.13 % (15806)Memory used [KB]: 3454
% 11.46/3.13 % (15806)Time elapsed: 0.098 s
% 11.46/3.13 % (15806)Instructions burned: 216 (million)
% 11.46/3.13 % (15806)------------------------------
% 11.46/3.13 % (15806)------------------------------
% 11.46/3.13 % (15809)Instruction limit reached!
% 11.46/3.13 % (15809)------------------------------
% 11.46/3.13 % (15809)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.46/3.13 % (15809)Termination reason: Unknown
% 11.46/3.13 % (15809)Termination phase: Preprocessing 3
% 11.46/3.13
% 11.46/3.13 % (15809)Memory used [KB]: 4093
% 11.46/3.13 % (15809)Time elapsed: 0.086 s
% 11.46/3.13 % (15809)Instructions burned: 183 (million)
% 11.46/3.13 % (15809)------------------------------
% 11.46/3.13 % (15809)------------------------------
% 12.02/3.14 % (15813)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_15624 for (2987ds/1021Mi)
% 12.02/3.14 % (15814)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_15624 for (2987ds/267Mi)
% 12.02/3.14 % (15815)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_15624 for (2987ds/204Mi)
% 12.02/3.15 % (15810)Instruction limit reached!
% 12.02/3.15 % (15810)------------------------------
% 12.02/3.15 % (15810)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.02/3.15 % (15810)Termination reason: Unknown
% 12.02/3.15 % (15810)Termination phase: Preprocessing 1
% 12.02/3.15
% 12.02/3.15 % (15810)Memory used [KB]: 3070
% 12.02/3.15 % (15810)Time elapsed: 0.077 s
% 12.02/3.15 % (15810)Instructions burned: 165 (million)
% 12.02/3.15 % (15810)------------------------------
% 12.02/3.15 % (15810)------------------------------
% 12.02/3.16 % (15816)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_15624 for (2987ds/26Mi)
% 12.02/3.18 % (15816)Instruction limit reached!
% 12.02/3.18 % (15816)------------------------------
% 12.02/3.18 % (15816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.02/3.18 % (15816)Termination reason: Unknown
% 12.02/3.18 % (15816)Termination phase: shuffling
% 12.02/3.18
% 12.02/3.18 % (15816)Memory used [KB]: 2174
% 12.02/3.18 % (15816)Time elapsed: 0.015 s
% 12.02/3.18 % (15816)Instructions burned: 28 (million)
% 12.02/3.18 % (15816)------------------------------
% 12.02/3.18 % (15816)------------------------------
% 12.02/3.19 % (15817)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_15624 for (2986ds/53Mi)
% 12.33/3.22 % (15817)Instruction limit reached!
% 12.33/3.22 % (15817)------------------------------
% 12.33/3.22 % (15817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.33/3.22 % (15817)Termination reason: Unknown
% 12.33/3.22 % (15817)Termination phase: shuffling
% 12.33/3.22
% 12.33/3.22 % (15817)Memory used [KB]: 2814
% 12.33/3.22 % (15817)Time elapsed: 0.027 s
% 12.33/3.22 % (15817)Instructions burned: 54 (million)
% 12.33/3.22 % (15817)------------------------------
% 12.33/3.22 % (15817)------------------------------
% 12.33/3.23 % (15815)Instruction limit reached!
% 12.33/3.23 % (15815)------------------------------
% 12.33/3.23 % (15815)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.33/3.23 % (15815)Termination reason: Unknown
% 12.33/3.23 % (15815)Termination phase: Property scanning
% 12.33/3.23
% 12.33/3.23 % (15815)Memory used [KB]: 3582
% 12.33/3.23 % (15815)Time elapsed: 0.091 s
% 12.33/3.23 % (15815)Instructions burned: 206 (million)
% 12.33/3.23 % (15815)------------------------------
% 12.33/3.23 % (15815)------------------------------
% 12.33/3.24 % (15818)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_15624 for (2986ds/4436Mi)
% 12.33/3.25 % (15819)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_15624 for (2986ds/1539Mi)
% 12.33/3.26 % (15814)Instruction limit reached!
% 12.33/3.26 % (15814)------------------------------
% 12.33/3.26 % (15814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.33/3.26 % (15814)Termination reason: Unknown
% 12.33/3.26 % (15814)Termination phase: Property scanning
% 12.33/3.26
% 12.33/3.26 % (15814)Memory used [KB]: 4093
% 12.33/3.26 % (15814)Time elapsed: 0.122 s
% 12.33/3.26 % (15814)Instructions burned: 267 (million)
% 12.33/3.26 % (15814)------------------------------
% 12.33/3.26 % (15814)------------------------------
% 12.33/3.28 % (15820)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_15624 for (2985ds/408Mi)
% 12.33/3.29 % (15812)Instruction limit reached!
% 12.33/3.29 % (15812)------------------------------
% 12.33/3.29 % (15812)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.33/3.29 % (15812)Termination reason: Unknown
% 12.33/3.29 % (15812)Termination phase: Saturation
% 12.33/3.29
% 12.33/3.29 % (15812)Memory used [KB]: 8955
% 12.33/3.29 % (15812)Time elapsed: 0.173 s
% 12.33/3.29 % (15812)Instructions burned: 368 (million)
% 12.33/3.29 % (15812)------------------------------
% 12.33/3.29 % (15812)------------------------------
% 12.90/3.30 % (15821)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_15624 for (2985ds/5205Mi)
% 13.00/3.40 % (15801)Instruction limit reached!
% 13.00/3.40 % (15801)------------------------------
% 13.00/3.40 % (15801)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.00/3.40 % (15801)Termination reason: Unknown
% 13.00/3.40 % (15801)Termination phase: Saturation
% 13.00/3.40
% 13.00/3.40 % (15801)Memory used [KB]: 9850
% 13.00/3.40 % (15801)Time elapsed: 0.503 s
% 13.00/3.40 % (15801)Instructions burned: 988 (million)
% 13.00/3.40 % (15801)------------------------------
% 13.00/3.40 % (15801)------------------------------
% 13.00/3.42 % (15822)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_15624 for (2984ds/1913Mi)
% 13.00/3.47 % (15820)Instruction limit reached!
% 13.00/3.47 % (15820)------------------------------
% 13.00/3.47 % (15820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.00/3.47 % (15820)Termination reason: Unknown
% 13.00/3.47 % (15820)Termination phase: Saturation
% 13.00/3.47
% 13.00/3.47 % (15820)Memory used [KB]: 6268
% 13.00/3.47 % (15820)Time elapsed: 0.194 s
% 13.00/3.47 % (15820)Instructions burned: 408 (million)
% 13.00/3.47 % (15820)------------------------------
% 13.00/3.47 % (15820)------------------------------
% 13.00/3.49 % (15808)Instruction limit reached!
% 13.00/3.49 % (15808)------------------------------
% 13.00/3.49 % (15808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.00/3.49 % (15808)Termination reason: Unknown
% 13.00/3.49 % (15808)Termination phase: Saturation
% 13.00/3.49
% 13.00/3.49 % (15808)Memory used [KB]: 8955
% 13.00/3.49 % (15808)Time elapsed: 0.449 s
% 13.00/3.49 % (15808)Instructions burned: 922 (million)
% 13.00/3.49 % (15808)------------------------------
% 13.00/3.49 % (15808)------------------------------
% 13.00/3.49 % (15823)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_15624 for (2983ds/4350Mi)
% 13.69/3.50 % (15824)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_15624 for (2983ds/68Mi)
% 13.69/3.54 % (15824)Instruction limit reached!
% 13.69/3.54 % (15824)------------------------------
% 13.69/3.54 % (15824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.69/3.54 % (15824)Termination reason: Unknown
% 13.69/3.54 % (15824)Termination phase: shuffling
% 13.69/3.54
% 13.69/3.54 % (15824)Memory used [KB]: 2814
% 13.69/3.54 % (15824)Time elapsed: 0.034 s
% 13.69/3.54 % (15824)Instructions burned: 68 (million)
% 13.69/3.54 % (15824)------------------------------
% 13.69/3.54 % (15824)------------------------------
% 13.69/3.54 % (15823)Refutation not found, incomplete strategy
% 13.69/3.54 % (15823)------------------------------
% 13.69/3.54 % (15823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.69/3.54 % (15823)Termination reason: Refutation not found, incomplete strategy
% 13.69/3.54
% 13.69/3.54
% 13.69/3.54 % (15823)Memory used [KB]: 7547
% 13.69/3.54 % (15823)Time elapsed: 0.057 s
% 13.69/3.54 % (15823)Instructions burned: 117 (million)
% 13.69/3.54 % (15823)------------------------------
% 13.69/3.54 % (15823)------------------------------
% 13.69/3.55 % (15825)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_15624 for (2983ds/358Mi)
% 13.69/3.56 % (15826)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_15624 for (2983ds/31Mi)
% 13.69/3.58 % (15826)Instruction limit reached!
% 13.69/3.58 % (15826)------------------------------
% 13.69/3.58 % (15826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.69/3.58 % (15826)Termination reason: Unknown
% 13.69/3.58 % (15826)Termination phase: shuffling
% 13.69/3.58
% 13.69/3.58 % (15826)Memory used [KB]: 2046
% 13.69/3.58 % (15826)Time elapsed: 0.017 s
% 13.69/3.58 % (15826)Instructions burned: 32 (million)
% 13.69/3.58 % (15826)------------------------------
% 13.69/3.58 % (15826)------------------------------
% 13.69/3.59 % (15827)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_15624 for (2982ds/279Mi)
% 13.83/3.64 % (15813)Instruction limit reached!
% 13.83/3.64 % (15813)------------------------------
% 13.83/3.64 % (15813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.83/3.64 % (15813)Termination reason: Unknown
% 13.83/3.64 % (15813)Termination phase: Saturation
% 13.83/3.64
% 13.83/3.64 % (15813)Memory used [KB]: 11129
% 13.83/3.64 % (15813)Time elapsed: 0.500 s
% 13.83/3.64 % (15813)Instructions burned: 1022 (million)
% 13.83/3.64 % (15813)------------------------------
% 13.83/3.64 % (15813)------------------------------
% 13.83/3.66 % (15828)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_15624 for (2982ds/258Mi)
% 14.35/3.72 % (15827)Instruction limit reached!
% 14.35/3.72 % (15827)------------------------------
% 14.35/3.72 % (15827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.35/3.72 % (15827)Termination reason: Unknown
% 14.35/3.72 % (15827)Termination phase: Saturation
% 14.35/3.72
% 14.35/3.72 % (15827)Memory used [KB]: 4221
% 14.35/3.72 % (15827)Time elapsed: 0.131 s
% 14.35/3.72 % (15827)Instructions burned: 279 (million)
% 14.35/3.72 % (15827)------------------------------
% 14.35/3.72 % (15827)------------------------------
% 14.35/3.72 % (15825)Instruction limit reached!
% 14.35/3.72 % (15825)------------------------------
% 14.35/3.72 % (15825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.35/3.72 % (15825)Termination reason: Unknown
% 14.35/3.72 % (15825)Termination phase: Saturation
% 14.35/3.72
% 14.35/3.72 % (15825)Memory used [KB]: 8699
% 14.35/3.72 % (15825)Time elapsed: 0.172 s
% 14.35/3.72 % (15825)Instructions burned: 358 (million)
% 14.35/3.72 % (15825)------------------------------
% 14.35/3.72 % (15825)------------------------------
% 14.35/3.74 % (15829)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_15624 for (2981ds/26Mi)
% 14.35/3.74 % (15830)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_15624 for (2981ds/995Mi)
% 14.35/3.75 % (15829)Instruction limit reached!
% 14.35/3.75 % (15829)------------------------------
% 14.35/3.75 % (15829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.35/3.75 % (15829)Termination reason: Unknown
% 14.35/3.75 % (15829)Termination phase: shuffling
% 14.35/3.75
% 14.35/3.75 % (15829)Memory used [KB]: 2174
% 14.35/3.75 % (15829)Time elapsed: 0.015 s
% 14.35/3.75 % (15829)Instructions burned: 27 (million)
% 14.35/3.75 % (15829)------------------------------
% 14.35/3.75 % (15829)------------------------------
% 14.35/3.77 % (15831)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_15624 for (2981ds/373Mi)
% 14.35/3.78 % (15828)Instruction limit reached!
% 14.35/3.78 % (15828)------------------------------
% 14.35/3.78 % (15828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.35/3.78 % (15828)Termination reason: Unknown
% 14.35/3.78 % (15828)Termination phase: Saturation
% 14.35/3.78
% 14.35/3.78 % (15828)Memory used [KB]: 8443
% 14.35/3.78 % (15828)Time elapsed: 0.121 s
% 14.35/3.78 % (15828)Instructions burned: 258 (million)
% 14.35/3.78 % (15828)------------------------------
% 14.35/3.78 % (15828)------------------------------
% 14.35/3.79 % (15832)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_15624 for (2980ds/253Mi)
% 14.86/3.91 % (15832)Instruction limit reached!
% 14.86/3.91 % (15832)------------------------------
% 14.86/3.91 % (15832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.86/3.91 % (15832)Termination reason: Unknown
% 14.86/3.91 % (15832)Termination phase: Property scanning
% 14.86/3.91
% 14.86/3.91 % (15832)Memory used [KB]: 4093
% 14.86/3.91 % (15832)Time elapsed: 0.117 s
% 14.86/3.91 % (15832)Instructions burned: 253 (million)
% 14.86/3.91 % (15832)------------------------------
% 14.86/3.91 % (15832)------------------------------
% 14.86/3.92 % (15833)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_15624 for (2979ds/832Mi)
% 14.86/3.95 % (15831)Instruction limit reached!
% 14.86/3.95 % (15831)------------------------------
% 14.86/3.95 % (15831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.86/3.95 % (15831)Termination reason: Unknown
% 14.86/3.95 % (15831)Termination phase: Saturation
% 14.86/3.95
% 14.86/3.95 % (15831)Memory used [KB]: 9338
% 14.86/3.95 % (15831)Time elapsed: 0.182 s
% 14.86/3.95 % (15831)Instructions burned: 373 (million)
% 14.86/3.95 % (15831)------------------------------
% 14.86/3.95 % (15831)------------------------------
% 14.86/3.97 % (15834)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_15624 for (2979ds/668Mi)
% 14.86/3.99 % (15819)Instruction limit reached!
% 14.86/3.99 % (15819)------------------------------
% 14.86/3.99 % (15819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.86/3.99 % (15819)Termination reason: Unknown
% 14.86/3.99 % (15819)Termination phase: Saturation
% 14.86/3.99
% 14.86/3.99 % (15819)Memory used [KB]: 11641
% 14.86/3.99 % (15819)Time elapsed: 0.745 s
% 14.86/3.99 % (15819)Instructions burned: 1539 (million)
% 14.86/3.99 % (15819)------------------------------
% 14.86/3.99 % (15819)------------------------------
% 14.86/4.01 % (15835)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_15624 for (2978ds/40Mi)
% 18.59/4.03 % (15835)Instruction limit reached!
% 18.59/4.03 % (15835)------------------------------
% 18.59/4.03 % (15835)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.59/4.03 % (15835)Termination reason: Unknown
% 18.59/4.03 % (15835)Termination phase: shuffling
% 18.59/4.03
% 18.59/4.03 % (15835)Memory used [KB]: 2430
% 18.59/4.03 % (15835)Time elapsed: 0.021 s
% 18.59/4.03 % (15835)Instructions burned: 40 (million)
% 18.59/4.03 % (15835)------------------------------
% 18.59/4.03 % (15835)------------------------------
% 18.59/4.04 % (15836)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_15624 for (2978ds/294Mi)
% 18.59/4.06 % (15822)Instruction limit reached!
% 18.59/4.06 % (15822)------------------------------
% 18.59/4.06 % (15822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.59/4.06 % (15822)Termination reason: Unknown
% 18.59/4.06 % (15822)Termination phase: Saturation
% 18.59/4.06
% 18.59/4.06 % (15822)Memory used [KB]: 4093
% 18.59/4.06 % (15822)Time elapsed: 0.642 s
% 18.59/4.06 % (15822)Instructions burned: 1914 (million)
% 18.59/4.06 % (15822)------------------------------
% 18.59/4.06 % (15822)------------------------------
% 18.59/4.08 % (15837)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_15624 for (2977ds/187Mi)
% 18.59/4.12 % (15833)Refutation not found, incomplete strategy
% 18.59/4.12 % (15833)------------------------------
% 18.59/4.12 % (15833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.59/4.12 % (15833)Termination reason: Refutation not found, incomplete strategy
% 18.59/4.12
% 18.59/4.12
% 18.59/4.12 % (15833)Memory used [KB]: 10362
% 18.59/4.12 % (15833)Time elapsed: 0.196 s
% 18.59/4.12 % (15833)Instructions burned: 404 (million)
% 18.59/4.12 % (15833)------------------------------
% 18.59/4.12 % (15833)------------------------------
% 19.14/4.14 % (15836)Refutation not found, incomplete strategy
% 19.14/4.14 % (15836)------------------------------
% 19.14/4.14 % (15836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.14/4.14 % (15836)Termination reason: Refutation not found, incomplete strategy
% 19.14/4.14
% 19.14/4.14
% 19.14/4.14 % (15836)Memory used [KB]: 7803
% 19.14/4.14 % (15836)Time elapsed: 0.092 s
% 19.14/4.14 % (15836)Instructions burned: 198 (million)
% 19.14/4.14 % (15836)------------------------------
% 19.14/4.14 % (15836)------------------------------
% 19.14/4.14 % (15838)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_15624 for (2977ds/371Mi)
% 19.14/4.15 % (15839)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_15624 for (2977ds/1827Mi)
% 19.14/4.17 % (15837)Instruction limit reached!
% 19.14/4.17 % (15837)------------------------------
% 19.14/4.17 % (15837)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.14/4.17 % (15837)Termination reason: Unknown
% 19.14/4.17 % (15837)Termination phase: Property scanning
% 19.14/4.17
% 19.14/4.17 % (15837)Memory used [KB]: 3709
% 19.14/4.17 % (15837)Time elapsed: 0.089 s
% 19.14/4.17 % (15837)Instructions burned: 187 (million)
% 19.14/4.17 % (15837)------------------------------
% 19.14/4.17 % (15837)------------------------------
% 19.14/4.18 % (15840)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_15624 for (2976ds/70Mi)
% 19.14/4.19 % (15830)Instruction limit reached!
% 19.14/4.19 % (15830)------------------------------
% 19.14/4.19 % (15830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.14/4.19 % (15830)Termination reason: Unknown
% 19.14/4.19 % (15830)Termination phase: Saturation
% 19.14/4.19
% 19.14/4.19 % (15830)Memory used [KB]: 9594
% 19.14/4.19 % (15830)Time elapsed: 0.455 s
% 19.14/4.19 % (15830)Instructions burned: 995 (million)
% 19.14/4.19 % (15830)------------------------------
% 19.14/4.19 % (15830)------------------------------
% 19.64/4.21 % (15841)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_15624 for (2976ds/316Mi)
% 19.64/4.22 % (15840)Instruction limit reached!
% 19.64/4.22 % (15840)------------------------------
% 19.64/4.22 % (15840)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.64/4.22 % (15840)Termination reason: Unknown
% 19.64/4.22 % (15840)Termination phase: shuffling
% 19.64/4.22
% 19.64/4.22 % (15840)Memory used [KB]: 2942
% 19.64/4.22 % (15840)Time elapsed: 0.035 s
% 19.64/4.22 % (15840)Instructions burned: 71 (million)
% 19.64/4.22 % (15840)------------------------------
% 19.64/4.22 % (15840)------------------------------
% 19.64/4.23 % (15842)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_15624 for (2976ds/932Mi)
% 19.64/4.28 % (15834)Instruction limit reached!
% 19.64/4.28 % (15834)------------------------------
% 19.64/4.28 % (15834)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.64/4.28 % (15834)Termination reason: Unknown
% 19.64/4.28 % (15834)Termination phase: Saturation
% 19.64/4.28
% 19.64/4.28 % (15834)Memory used [KB]: 14072
% 19.64/4.28 % (15834)Time elapsed: 0.311 s
% 19.64/4.28 % (15834)Instructions burned: 668 (million)
% 19.64/4.28 % (15834)------------------------------
% 19.64/4.28 % (15834)------------------------------
% 19.64/4.29 % (15843)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_15624 for (2975ds/4714Mi)
% 19.97/4.31 % (15838)Instruction limit reached!
% 19.97/4.31 % (15838)------------------------------
% 19.97/4.31 % (15838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.97/4.31 % (15838)Termination reason: Unknown
% 19.97/4.31 % (15838)Termination phase: Saturation
% 19.97/4.31
% 19.97/4.31 % (15838)Memory used [KB]: 8955
% 19.97/4.31 % (15838)Time elapsed: 0.178 s
% 19.97/4.31 % (15838)Instructions burned: 372 (million)
% 19.97/4.31 % (15838)------------------------------
% 19.97/4.31 % (15838)------------------------------
% 19.97/4.33 % (15844)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_15624 for (2975ds/8250Mi)
% 19.97/4.35 % (15841)Instruction limit reached!
% 19.97/4.35 % (15841)------------------------------
% 19.97/4.35 % (15841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.97/4.35 % (15841)Termination reason: Unknown
% 19.97/4.35 % (15841)Termination phase: Saturation
% 19.97/4.35
% 19.97/4.35 % (15841)Memory used [KB]: 4477
% 19.97/4.35 % (15841)Time elapsed: 0.144 s
% 19.97/4.35 % (15841)Instructions burned: 316 (million)
% 19.97/4.35 % (15841)------------------------------
% 19.97/4.35 % (15841)------------------------------
% 19.97/4.37 % (15845)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_15624 for (2975ds/770Mi)
% 20.53/4.43 % (15845)Refutation not found, incomplete strategy
% 20.53/4.43 % (15845)------------------------------
% 20.53/4.43 % (15845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.53/4.43 % (15845)Termination reason: Refutation not found, incomplete strategy
% 20.53/4.43
% 20.53/4.43
% 20.53/4.43 % (15845)Memory used [KB]: 7675
% 20.53/4.43 % (15845)Time elapsed: 0.059 s
% 20.53/4.43 % (15845)Instructions burned: 121 (million)
% 20.53/4.43 % (15845)------------------------------
% 20.53/4.43 % (15845)------------------------------
% 20.53/4.45 % (15846)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_15624 for (2974ds/794Mi)
% 20.81/4.52 % (15843)Refutation not found, incomplete strategy
% 20.81/4.52 % (15843)------------------------------
% 20.81/4.52 % (15843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.81/4.52 % (15843)Termination reason: Refutation not found, incomplete strategy
% 20.81/4.52
% 20.81/4.52
% 20.81/4.52 % (15843)Memory used [KB]: 9722
% 20.81/4.52 % (15843)Time elapsed: 0.225 s
% 20.81/4.52 % (15843)Instructions burned: 485 (million)
% 20.81/4.52 % (15843)------------------------------
% 20.81/4.52 % (15843)------------------------------
% 20.81/4.53 % (15847)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_15624 for (2973ds/464Mi)
% 20.81/4.56 % (15821)First to succeed.
% 20.81/4.57 % (15821)Refutation found. Thanks to Tanya!
% 20.81/4.57 % SZS status Theorem for DTF2THF_15624
% 20.81/4.57 % SZS output start Proof for DTF2THF_15624
% 20.81/4.57 thf(type_def_6, type, proces554692349s_term: ($tType * $tType) > $tType).
% 20.81/4.57 thf(type_def_7, type, product_prod: ($tType * $tType) > $tType).
% 20.81/4.57 thf(type_def_8, type, proces634752977rocess: ($tType) > $tType).
% 20.81/4.57 thf(type_def_9, type, set: ($tType) > $tType).
% 20.81/4.57 thf(type_def_10, type, itself: ($tType) > $tType).
% 20.81/4.57 thf(type_def_11, type, a: $tType).
% 20.81/4.57 thf(type_def_12, type, b: $tType).
% 20.81/4.57 thf(func_def_0, type, proces554692349s_term: ($tType * $tType) > $tType).
% 20.81/4.57 thf(func_def_1, type, proces634752977rocess: ($tType) > $tType).
% 20.81/4.57 thf(func_def_2, type, product_prod: ($tType * $tType) > $tType).
% 20.81/4.57 thf(func_def_3, type, set: ($tType) > $tType).
% 20.81/4.57 thf(func_def_4, type, itself: ($tType) > $tType).
% 20.81/4.57 thf(func_def_5, type, b: $tType).
% 20.81/4.57 thf(func_def_6, type, a: $tType).
% 20.81/4.57 thf(func_def_7, type, bNF_rel_fun: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > X1 > $o) > (X2 > X3 > $o) > (X0 > X2) > (X1 > X3) > $o)).
% 20.81/4.57 thf(func_def_8, type, undefined: !>[X0: $tType]:(X0)).
% 20.81/4.57 thf(func_def_9, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 20.81/4.57 thf(func_def_10, type, proces1239275103le_CH1: !>[X0: $tType, X1: $tType]:((X0 > proces554692349s_term @ X1 @ X0) > proces554692349s_term @ X1 @ X0 > proces554692349s_term @ X1 @ X0)).
% 20.81/4.57 thf(func_def_11, type, proces1869379930H1_rel: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > proces554692349s_term @ X1 @ X0) @ proces554692349s_term @ X1 @ X0 > product_prod @ (X0 > proces554692349s_term @ X1 @ X0) @ proces554692349s_term @ X1 @ X0 > $o)).
% 20.81/4.57 thf(func_def_12, type, proces1239275104le_CH2: !>[X0: $tType, X1: $tType]:((X0 > proces554692349s_term @ X1 @ X0) > proces554692349s_term @ X1 @ X0 > proces554692349s_term @ X1 @ X0)).
% 20.81/4.57 thf(func_def_13, type, proces93903513H2_rel: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > proces554692349s_term @ X1 @ X0) @ proces554692349s_term @ X1 @ X0 > product_prod @ (X0 > proces554692349s_term @ X1 @ X0) @ proces554692349s_term @ X1 @ X0 > $o)).
% 20.81/4.57 thf(func_def_14, type, proces126235999e_CONT: !>[X0: $tType, X1: $tType]:((X0 > proces554692349s_term @ X1 @ X0) > proces554692349s_term @ X1 @ X0 > proces554692349s_term @ X1 @ X0)).
% 20.81/4.57 thf(func_def_15, type, proces1004198490NT_rel: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > proces554692349s_term @ X1 @ X0) @ proces554692349s_term @ X1 @ X0 > product_prod @ (X0 > proces554692349s_term @ X1 @ X0) @ proces554692349s_term @ X1 @ X0 > $o)).
% 20.81/4.57 thf(func_def_16, type, proces1708129104e_PREF: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > proces554692349s_term @ X1 @ X2) > proces554692349s_term @ X1 @ X0 > X1)).
% 20.81/4.57 thf(func_def_17, type, proces527360425EF_rel: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ (X0 > proces554692349s_term @ X1 @ X2) @ proces554692349s_term @ X1 @ X0 > product_prod @ (X0 > proces554692349s_term @ X1 @ X2) @ proces554692349s_term @ X1 @ X0 > $o)).
% 20.81/4.57 thf(func_def_18, type, proces1121166967uarded: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > proces554692349s_term @ X1 @ X2) > $o)).
% 20.81/4.57 thf(func_def_19, type, proces687458811_isACT: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > proces554692349s_term @ X1 @ X2) > proces554692349s_term @ X3 @ X0 > $o)).
% 20.81/4.57 thf(func_def_20, type, proces896239806CT_rel: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ (X0 > proces554692349s_term @ X1 @ X2) @ proces554692349s_term @ X3 @ X0 > product_prod @ (X0 > proces554692349s_term @ X1 @ X2) @ proces554692349s_term @ X3 @ X0 > $o)).
% 20.81/4.57 thf(func_def_21, type, proces1525233512Action: !>[X0: $tType]:(X0 > proces634752977rocess @ X0 > proces634752977rocess @ X0)).
% 20.81/4.57 thf(func_def_22, type, proces1915862579Choice: !>[X0: $tType]:(proces634752977rocess @ X0 > proces634752977rocess @ X0 > proces634752977rocess @ X0)).
% 20.81/4.57 thf(func_def_23, type, proces1406508781rocess: !>[X0: $tType, X1: $tType]:((X0 > proces634752977rocess @ X0 > X1) > (proces634752977rocess @ X0 > proces634752977rocess @ X0 > X1) > proces634752977rocess @ X0 > X1)).
% 20.81/4.57 thf(func_def_24, type, proces979765041_ch1Of: !>[X0: $tType]:(proces634752977rocess @ X0 > proces634752977rocess @ X0)).
% 20.81/4.57 thf(func_def_25, type, proces988026546_ch2Of: !>[X0: $tType]:(proces634752977rocess @ X0 > proces634752977rocess @ X0)).
% 20.81/4.57 thf(func_def_26, type, proces1778668539contOf: !>[X0: $tType]:(proces634752977rocess @ X0 > proces634752977rocess @ X0)).
% 20.81/4.57 thf(func_def_27, type, proces894737309rocess: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X0 > X1) > (X0 > $o) > (X0 > proces634752977rocess @ X1) > (X0 > X0) > (X0 > $o) > (X0 > proces634752977rocess @ X1) > (X0 > X0) > (X0 > $o) > (X0 > proces634752977rocess @ X1) > (X0 > X0) > X0 > proces634752977rocess @ X1)).
% 20.81/4.57 thf(func_def_28, type, proces10484146Action: !>[X0: $tType]:(proces634752977rocess @ X0 > $o)).
% 20.81/4.57 thf(func_def_29, type, proces401113213Choice: !>[X0: $tType]:(proces634752977rocess @ X0 > $o)).
% 20.81/4.57 thf(func_def_30, type, proces370407749rocess: !>[X0: $tType, X1: $tType]:((X0 > X1) > proces634752977rocess @ X0 > proces634752977rocess @ X1)).
% 20.81/4.57 thf(func_def_31, type, proces1205983068rocess: !>[X0: $tType]:((X0 > $o) > proces634752977rocess @ X0 > $o)).
% 20.81/4.57 thf(func_def_32, type, proces745025900prefOf: !>[X0: $tType]:(proces634752977rocess @ X0 > X0)).
% 20.81/4.57 thf(func_def_33, type, proces749077512rocess: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > proces634752977rocess @ X0 > proces634752977rocess @ X1 > $o)).
% 20.81/4.57 thf(func_def_34, type, proces1454156180ss_ACT: !>[X0: $tType, X1: $tType]:(X0 > proces554692349s_term @ X0 @ X1 > proces554692349s_term @ X0 @ X1)).
% 20.81/4.57 thf(func_def_35, type, proces89589571ess_CH: !>[X0: $tType, X1: $tType]:(proces554692349s_term @ X0 @ X1 > proces554692349s_term @ X0 @ X1 > proces554692349s_term @ X0 @ X1)).
% 20.81/4.57 thf(func_def_36, type, proces1062592052s_PROC: !>[X0: $tType, X1: $tType]:(proces634752977rocess @ X0 > proces554692349s_term @ X0 @ X1)).
% 20.81/4.57 thf(func_def_37, type, proces1627516585ss_VAR: !>[X0: $tType, X1: $tType]:(X0 > proces554692349s_term @ X1 @ X0)).
% 20.81/4.57 thf(func_def_38, type, proces460752237s_term: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1) > (proces634752977rocess @ X2 > X1) > (X2 > proces554692349s_term @ X2 @ X0 > X1) > (proces554692349s_term @ X2 @ X0 > proces554692349s_term @ X2 @ X0 > X1) > proces554692349s_term @ X2 @ X0 > X1)).
% 20.81/4.57 thf(func_def_39, type, proces224683037s_term: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > X1) > (X2 > X3) > proces554692349s_term @ X0 @ X2 > proces554692349s_term @ X1 @ X3)).
% 20.81/4.57 thf(func_def_40, type, proces2118920028s_term: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X1 > $o) > proces554692349s_term @ X0 @ X1 > $o)).
% 20.81/4.57 thf(func_def_41, type, proces2117273769s_term: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1) > (proces634752977rocess @ X2 > X1) > (X2 > proces554692349s_term @ X2 @ X0 > X1 > X1) > (proces554692349s_term @ X2 @ X0 > proces554692349s_term @ X2 @ X0 > X1 > X1 > X1) > proces554692349s_term @ X2 @ X0 > X1)).
% 20.81/4.57 thf(func_def_42, type, proces2029722208s_term: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > X1 > $o) > (X2 > X3 > $o) > proces554692349s_term @ X0 @ X2 > proces554692349s_term @ X1 @ X3 > $o)).
% 20.81/4.57 thf(func_def_43, type, proces1493547885s_term: !>[X0: $tType, X1: $tType]:(proces554692349s_term @ X0 @ X1 > set @ X1)).
% 20.81/4.57 thf(func_def_44, type, proces1652378886lution: !>[X0: $tType, X1: $tType]:((X0 > proces554692349s_term @ X1 @ X0) > proces554692349s_term @ X1 @ X0 > proces634752977rocess @ X1)).
% 20.81/4.57 thf(func_def_45, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 20.81/4.57 thf(func_def_46, type, product_curry: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X1 > X2) > X0 > X1 > X2)).
% 20.81/4.57 thf(func_def_47, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 20.81/4.57 thf(func_def_48, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 20.81/4.57 thf(func_def_49, type, type: !>[X0: $tType]:(itself @ X0)).
% 20.81/4.57 thf(func_def_50, type, inv_image: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X0 @ X0 > (X1 > X0) > set @ product_prod @ X1 @ X1)).
% 20.81/4.57 thf(func_def_51, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 20.81/4.57 thf(func_def_52, type, acc: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ X0)).
% 20.81/4.57 thf(func_def_53, type, accp: !>[X0: $tType]:((X0 > X0 > $o) > X0 > $o)).
% 20.81/4.57 thf(func_def_54, type, lex_prod: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X0 @ X0 > set @ product_prod @ X1 @ X1 > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1)).
% 20.81/4.57 thf(func_def_55, type, adm_wf: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X0 @ X0 > ((X0 > X1) > X0 > X1) > $o)).
% 20.81/4.57 thf(func_def_56, type, cut: !>[X0: $tType, X1: $tType]:((X0 > X1) > set @ product_prod @ X0 @ X0 > X0 > X0 > X1)).
% 20.81/4.57 thf(func_def_57, type, same_fst: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X0 > set @ product_prod @ X1 @ X1) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1)).
% 20.81/4.57 thf(func_def_58, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 20.81/4.57 thf(func_def_59, type, a2: a).
% 20.81/4.57 thf(func_def_60, type, a3: a).
% 20.81/4.57 thf(func_def_61, type, p: proces634752977rocess @ a).
% 20.81/4.57 thf(func_def_62, type, p2: proces634752977rocess @ a).
% 20.81/4.57 thf(func_def_63, type, pa: proces634752977rocess @ a).
% 20.81/4.57 thf(func_def_64, type, q: proces634752977rocess @ a).
% 20.81/4.57 thf(func_def_65, type, sys: b > proces554692349s_term @ a @ b).
% 20.81/4.57 thf(func_def_90, type, ph1: !>[X0: $tType]:(X0)).
% 20.81/4.57 thf(func_def_91, type, sK2: !>[X0: $tType, X1: $tType]:(product_prod @ X1 @ X0 > X0)).
% 20.81/4.57 thf(func_def_92, type, sK3: !>[X0: $tType, X1: $tType]:(product_prod @ X1 @ X0 > X1)).
% 20.81/4.57 thf(func_def_93, type, sK4: !>[X0: $tType, X1: $tType]:(product_prod @ X1 @ X0 > X0)).
% 20.81/4.57 thf(func_def_94, type, sK5: !>[X0: $tType, X1: $tType]:(product_prod @ X1 @ X0 > X1)).
% 20.81/4.57 thf(f3865,plain,(
% 20.81/4.57 $false),
% 20.81/4.57 inference(avatar_sat_refutation,[status(thm)],[f2759,f3861])).
% 20.81/4.57 thf(f3861,plain,(
% 20.81/4.57 ~spl0_1),
% 20.81/4.57 inference(avatar_contradiction_clause,[status(thm)],[f3860])).
% 20.81/4.57 thf(f3860,plain,(
% 20.81/4.57 $false | ~spl0_1),
% 20.81/4.57 inference(subsumption_resolution,[status(thm)],[f3859,f2760])).
% 20.81/4.57 thf(f2760,plain,(
% 20.81/4.57 (p2 != (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa))) | ~spl0_1),
% 20.81/4.57 inference(equality_proxy_clausification,[status(thm)],[f2108])).
% 20.81/4.57 thf(f2108,plain,(
% 20.81/4.57 ($false = (p2 = (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa)))) | ~spl0_1),
% 20.81/4.57 inference(avatar_component_clause,[status(thm)],[f2107])).
% 20.81/4.57 thf(f2107,definition,(
% 20.81/4.57 spl0_1 <=> ($false = (p2 = (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa))))),
% 20.81/4.57 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 20.81/4.57 thf(f3859,plain,(
% 20.81/4.57 (p2 = (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa)))),
% 20.81/4.57 inference(forward_demodulation,[status(thm)],[f3857,f1806])).
% 20.81/4.57 thf(f1806,plain,(
% 20.81/4.57 ( ! [X0 : $tType,X2 : X0,X1 : proces634752977rocess @ X0] : (((proces1778668539contOf @ X0 @ (proces1525233512Action @ X0 @ X2 @ X1)) = X1)) )),
% 20.81/4.57 inference(equality_proxy_clausification,[status(thm)],[f1805])).
% 20.81/4.57 thf(f1805,plain,(
% 20.81/4.57 ( ! [X0 : $tType,X2 : X0,X1 : proces634752977rocess @ X0] : (($true = ((proces1778668539contOf @ X0 @ (proces1525233512Action @ X0 @ X2 @ X1)) = X1))) )),
% 20.81/4.57 inference(beta_eta_normalization,[status(thm)],[f1804])).
% 20.81/4.57 thf(f1804,plain,(
% 20.81/4.57 ( ! [X0 : $tType,X2 : X0,X1 : proces634752977rocess @ X0] : (($true = ((^[Y0 : X0]: ((proces1778668539contOf @ X0 @ (proces1525233512Action @ X0 @ Y0 @ X1)) = X1)) @ X2))) )),
% 20.81/4.57 inference(pi_clausification,[status(thm)],[f1803])).
% 20.81/4.57 thf(f1803,plain,(
% 20.81/4.57 ( ! [X0 : $tType,X1 : proces634752977rocess @ X0] : (($true = (!! @ X0 @ (^[Y0 : X0]: ((proces1778668539contOf @ X0 @ (proces1525233512Action @ X0 @ Y0 @ X1)) = X1))))) )),
% 20.81/4.57 inference(beta_eta_normalization,[status(thm)],[f1802])).
% 20.81/4.57 thf(f1802,plain,(
% 20.81/4.57 ( ! [X0 : $tType,X1 : proces634752977rocess @ X0] : (($true = ((^[Y0 : proces634752977rocess @ X0]: (!! @ X0 @ (^[Y1 : X0]: ((proces1778668539contOf @ X0 @ (proces1525233512Action @ X0 @ Y1 @ Y0)) = Y0)))) @ X1))) )),
% 20.81/4.57 inference(pi_clausification,[status(thm)],[f1587])).
% 20.81/4.57 thf(f1587,plain,(
% 20.81/4.57 ( ! [X0 : $tType] : (((!! @ proces634752977rocess @ X0 @ (^[Y0 : proces634752977rocess @ X0]: (!! @ X0 @ (^[Y1 : X0]: ((proces1778668539contOf @ X0 @ (proces1525233512Action @ X0 @ Y1 @ Y0)) = Y0))))) = $true)) )),
% 20.81/4.57 inference(cnf_transformation,[status(thm)],[f790])).
% 20.81/4.57 thf(f790,plain,(
% 20.81/4.57 ! [X0 : $tType] : ((!! @ proces634752977rocess @ X0 @ (^[Y0 : proces634752977rocess @ X0]: (!! @ X0 @ (^[Y1 : X0]: ((proces1778668539contOf @ X0 @ (proces1525233512Action @ X0 @ Y1 @ Y0)) = Y0))))) = $true)),
% 20.81/4.57 inference(closure,[status(thm)],[f280])).
% 20.81/4.57 thf(f280,plain,(
% 20.81/4.57 ( ! [X0 : $tType] : (((!! @ proces634752977rocess @ X0 @ (^[Y0 : proces634752977rocess @ X0]: (!! @ X0 @ (^[Y1 : X0]: ((proces1778668539contOf @ X0 @ (proces1525233512Action @ X0 @ Y1 @ Y0)) = Y0))))) = $true)) )),
% 20.81/4.57 inference(fool_elimination,[status(thm)],[f279])).
% 20.81/4.57 thf(f279,plain,(
% 20.81/4.57 ! [X0 : $tType,X1 : X0,X2 : proces634752977rocess @ X0] : ((proces1778668539contOf @ X0 @ (proces1525233512Action @ X0 @ X1 @ X2)) = X2)),
% 20.81/4.57 inference(rectify,[status(thm)],[f72])).
% 20.81/4.57 thf(f72,axiom,(
% 20.81/4.57 ! [X0 : $tType,X36 : X0,X37 : proces634752977rocess @ X0] : ((proces1778668539contOf @ X0 @ (proces1525233512Action @ X0 @ X36 @ X37)) = X37)),
% 20.81/4.57 file('/export/starexec/sandbox/tmp/tmp.sFYK9PDrEK/DTF2THF_15624.p',fact_71_process_Osel_I2_J)).
% 20.81/4.57 thf(f3857,plain,(
% 20.81/4.57 (p2 = (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ (proces1778668539contOf @ a @ (proces1525233512Action @ a @ a2 @ pa)))))),
% 20.81/4.57 inference(backward_demodulation,[status(thm)],[f2754,f3854])).
% 20.81/4.57 thf(f3854,plain,(
% 20.81/4.57 ( ! [X1 : $tType,X0 : $tType,X2 : proces634752977rocess @ X1,X3 : X0 > proces554692349s_term @ X1 @ X0] : (((proces126235999e_CONT @ X0 @ X1 @ X3 @ (proces1062592052s_PROC @ X1 @ X0 @ X2)) = (proces1062592052s_PROC @ X1 @ X0 @ (proces1778668539contOf @ X1 @ X2)))) )),
% 20.81/4.57 inference(equality_proxy_clausification,[status(thm)],[f3853])).
% 20.81/4.57 thf(f3853,plain,(
% 20.81/4.57 ( ! [X1 : $tType,X0 : $tType,X2 : proces634752977rocess @ X1,X3 : X0 > proces554692349s_term @ X1 @ X0] : ((((proces126235999e_CONT @ X0 @ X1 @ X3 @ (proces1062592052s_PROC @ X1 @ X0 @ X2)) = (proces1062592052s_PROC @ X1 @ X0 @ (proces1778668539contOf @ X1 @ X2))) = $true)) )),
% 20.81/4.57 inference(beta_eta_normalization,[status(thm)],[f3852])).
% 20.81/4.57 thf(f3852,plain,(
% 20.81/4.57 ( ! [X1 : $tType,X0 : $tType,X2 : proces634752977rocess @ X1,X3 : X0 > proces554692349s_term @ X1 @ X0] : (($true = ((^[Y0 : X0 > proces554692349s_term @ X1 @ X0]: ((proces126235999e_CONT @ X0 @ X1 @ Y0 @ (proces1062592052s_PROC @ X1 @ X0 @ X2)) = (proces1062592052s_PROC @ X1 @ X0 @ (proces1778668539contOf @ X1 @ X2)))) @ X3))) )),
% 20.81/4.57 inference(pi_clausification,[status(thm)],[f3851])).
% 20.81/4.57 thf(f3851,plain,(
% 20.81/4.57 ( ! [X1 : $tType,X0 : $tType,X2 : proces634752977rocess @ X1] : (($true = (!! @ (X0 > proces554692349s_term @ X1 @ X0) @ (^[Y0 : X0 > proces554692349s_term @ X1 @ X0]: ((proces126235999e_CONT @ X0 @ X1 @ Y0 @ (proces1062592052s_PROC @ X1 @ X0 @ X2)) = (proces1062592052s_PROC @ X1 @ X0 @ (proces1778668539contOf @ X1 @ X2))))))) )),
% 20.81/4.57 inference(beta_eta_normalization,[status(thm)],[f3850])).
% 20.81/4.57 thf(f3850,plain,(
% 20.81/4.57 ( ! [X1 : $tType,X0 : $tType,X2 : proces634752977rocess @ X1] : ((((^[Y0 : proces634752977rocess @ X1]: (!! @ (X0 > proces554692349s_term @ X1 @ X0) @ (^[Y1 : X0 > proces554692349s_term @ X1 @ X0]: ((proces126235999e_CONT @ X0 @ X1 @ Y1 @ (proces1062592052s_PROC @ X1 @ X0 @ Y0)) = (proces1062592052s_PROC @ X1 @ X0 @ (proces1778668539contOf @ X1 @ Y0)))))) @ X2) = $true)) )),
% 20.81/4.57 inference(pi_clausification,[status(thm)],[f1448])).
% 20.81/4.57 thf(f1448,plain,(
% 20.81/4.57 ( ! [X1 : $tType,X0 : $tType] : (((!! @ proces634752977rocess @ X1 @ (^[Y0 : proces634752977rocess @ X1]: (!! @ (X0 > proces554692349s_term @ X1 @ X0) @ (^[Y1 : X0 > proces554692349s_term @ X1 @ X0]: ((proces126235999e_CONT @ X0 @ X1 @ Y1 @ (proces1062592052s_PROC @ X1 @ X0 @ Y0)) = (proces1062592052s_PROC @ X1 @ X0 @ (proces1778668539contOf @ X1 @ Y0))))))) = $true)) )),
% 20.81/4.57 inference(cnf_transformation,[status(thm)],[f1242])).
% 20.81/4.57 thf(f1242,plain,(
% 20.81/4.57 ! [X0 : $tType,X1 : $tType] : ((!! @ proces634752977rocess @ X1 @ (^[Y0 : proces634752977rocess @ X1]: (!! @ (X0 > proces554692349s_term @ X1 @ X0) @ (^[Y1 : X0 > proces554692349s_term @ X1 @ X0]: ((proces126235999e_CONT @ X0 @ X1 @ Y1 @ (proces1062592052s_PROC @ X1 @ X0 @ Y0)) = (proces1062592052s_PROC @ X1 @ X0 @ (proces1778668539contOf @ X1 @ Y0))))))) = $true)),
% 20.81/4.57 inference(rectify,[status(thm)],[f961])).
% 20.81/4.57 thf(f961,plain,(
% 20.81/4.57 ! [X1 : $tType,X0 : $tType] : ($true = (!! @ proces634752977rocess @ X0 @ (^[Y0 : proces634752977rocess @ X0]: (!! @ (X1 > proces554692349s_term @ X0 @ X1) @ (^[Y1 : X1 > proces554692349s_term @ X0 @ X1]: ((proces126235999e_CONT @ X1 @ X0 @ Y1 @ (proces1062592052s_PROC @ X0 @ X1 @ Y0)) = (proces1062592052s_PROC @ X0 @ X1 @ (proces1778668539contOf @ X0 @ Y0))))))))),
% 20.81/4.57 inference(closure,[status(thm)],[f960])).
% 20.81/4.57 thf(f960,plain,(
% 20.81/4.57 ( ! [X1 : $tType,X0 : $tType] : (($true = (!! @ proces634752977rocess @ X0 @ (^[Y0 : proces634752977rocess @ X0]: (!! @ (X1 > proces554692349s_term @ X0 @ X1) @ (^[Y1 : X1 > proces554692349s_term @ X0 @ X1]: ((proces126235999e_CONT @ X1 @ X0 @ Y1 @ (proces1062592052s_PROC @ X0 @ X1 @ Y0)) = (proces1062592052s_PROC @ X0 @ X1 @ (proces1778668539contOf @ X0 @ Y0))))))))) )),
% 20.81/4.57 inference(rectify,[status(thm)],[f482])).
% 20.81/4.57 thf(f482,plain,(
% 20.81/4.57 ( ! [X1 : $tType,X0 : $tType] : (((!! @ proces634752977rocess @ X1 @ (^[Y0 : proces634752977rocess @ X1]: (!! @ (X0 > proces554692349s_term @ X1 @ X0) @ (^[Y1 : X0 > proces554692349s_term @ X1 @ X0]: ((proces126235999e_CONT @ X0 @ X1 @ Y1 @ (proces1062592052s_PROC @ X1 @ X0 @ Y0)) = (proces1062592052s_PROC @ X1 @ X0 @ (proces1778668539contOf @ X1 @ Y0))))))) = $true)) )),
% 20.81/4.57 inference(fool_elimination,[status(thm)],[f481])).
% 20.81/4.57 thf(f481,plain,(
% 20.81/4.57 ! [X0 : $tType,X1 : $tType,X2 : X0 > proces554692349s_term @ X1 @ X0,X3 : proces634752977rocess @ X1] : ((proces126235999e_CONT @ X0 @ X1 @ X2 @ (proces1062592052s_PROC @ X1 @ X0 @ X3)) = (proces1062592052s_PROC @ X1 @ X0 @ (proces1778668539contOf @ X1 @ X3)))),
% 20.81/4.57 inference(rectify,[status(thm)],[f77])).
% 20.81/4.57 thf(f77,axiom,(
% 20.81/4.57 ! [X0 : $tType,X2 : $tType,X25 : X0 > proces554692349s_term @ X2 @ X0,X27 : proces634752977rocess @ X2] : ((proces126235999e_CONT @ X0 @ X2 @ X25 @ (proces1062592052s_PROC @ X2 @ X0 @ X27)) = (proces1062592052s_PROC @ X2 @ X0 @ (proces1778668539contOf @ X2 @ X27)))),
% 20.81/4.57 file('/export/starexec/sandbox/tmp/tmp.sFYK9PDrEK/DTF2THF_15624.p',fact_76_CONT_Osimps_I2_J)).
% 20.81/4.57 thf(f2754,plain,(
% 20.81/4.57 (p2 = (proces1652378886lution @ b @ a @ sys @ (proces126235999e_CONT @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ (proces1525233512Action @ a @ a2 @ pa)))))),
% 20.81/4.57 inference(backward_demodulation,[status(thm)],[f2751,f2748])).
% 20.81/4.57 thf(f2748,plain,(
% 20.81/4.57 (a2 = a3)),
% 20.81/4.57 inference(forward_demodulation,[status(thm)],[f2734,f1792])).
% 20.81/4.57 thf(f1792,plain,(
% 20.81/4.57 ( ! [X0 : $tType,X2 : X0,X1 : proces634752977rocess @ X0] : (((proces745025900prefOf @ X0 @ (proces1525233512Action @ X0 @ X2 @ X1)) = X2)) )),
% 20.81/4.57 inference(equality_proxy_clausification,[status(thm)],[f1791])).
% 20.81/4.57 thf(f1791,plain,(
% 20.81/4.57 ( ! [X0 : $tType,X2 : X0,X1 : proces634752977rocess @ X0] : (($true = ((proces745025900prefOf @ X0 @ (proces1525233512Action @ X0 @ X2 @ X1)) = X2))) )),
% 20.81/4.57 inference(beta_eta_normalization,[status(thm)],[f1790])).
% 20.81/4.57 thf(f1790,plain,(
% 20.81/4.57 ( ! [X0 : $tType,X2 : X0,X1 : proces634752977rocess @ X0] : ((((^[Y0 : X0]: ((proces745025900prefOf @ X0 @ (proces1525233512Action @ X0 @ Y0 @ X1)) = Y0)) @ X2) = $true)) )),
% 20.81/4.57 inference(pi_clausification,[status(thm)],[f1789])).
% 20.81/4.57 thf(f1789,plain,(
% 20.81/4.57 ( ! [X0 : $tType,X1 : proces634752977rocess @ X0] : (($true = (!! @ X0 @ (^[Y0 : X0]: ((proces745025900prefOf @ X0 @ (proces1525233512Action @ X0 @ Y0 @ X1)) = Y0))))) )),
% 20.81/4.57 inference(beta_eta_normalization,[status(thm)],[f1788])).
% 20.81/4.57 thf(f1788,plain,(
% 20.81/4.57 ( ! [X0 : $tType,X1 : proces634752977rocess @ X0] : (($true = ((^[Y0 : proces634752977rocess @ X0]: (!! @ X0 @ (^[Y1 : X0]: ((proces745025900prefOf @ X0 @ (proces1525233512Action @ X0 @ Y1 @ Y0)) = Y1)))) @ X1))) )),
% 20.81/4.57 inference(pi_clausification,[status(thm)],[f1517])).
% 20.81/4.57 thf(f1517,plain,(
% 20.81/4.57 ( ! [X0 : $tType] : (((!! @ proces634752977rocess @ X0 @ (^[Y0 : proces634752977rocess @ X0]: (!! @ X0 @ (^[Y1 : X0]: ((proces745025900prefOf @ X0 @ (proces1525233512Action @ X0 @ Y1 @ Y0)) = Y1))))) = $true)) )),
% 20.81/4.57 inference(cnf_transformation,[status(thm)],[f839])).
% 20.81/4.57 thf(f839,plain,(
% 20.81/4.57 ! [X0 : $tType] : ((!! @ proces634752977rocess @ X0 @ (^[Y0 : proces634752977rocess @ X0]: (!! @ X0 @ (^[Y1 : X0]: ((proces745025900prefOf @ X0 @ (proces1525233512Action @ X0 @ Y1 @ Y0)) = Y1))))) = $true)),
% 20.81/4.57 inference(closure,[status(thm)],[f338])).
% 20.81/4.57 thf(f338,plain,(
% 20.81/4.57 ( ! [X0 : $tType] : (((!! @ proces634752977rocess @ X0 @ (^[Y0 : proces634752977rocess @ X0]: (!! @ X0 @ (^[Y1 : X0]: ((proces745025900prefOf @ X0 @ (proces1525233512Action @ X0 @ Y1 @ Y0)) = Y1))))) = $true)) )),
% 20.81/4.57 inference(fool_elimination,[status(thm)],[f337])).
% 20.81/4.57 thf(f337,plain,(
% 20.81/4.57 ! [X0 : $tType,X1 : X0,X2 : proces634752977rocess @ X0] : ((proces745025900prefOf @ X0 @ (proces1525233512Action @ X0 @ X1 @ X2)) = X1)),
% 20.81/4.57 inference(rectify,[status(thm)],[f28])).
% 20.81/4.57 thf(f28,axiom,(
% 20.81/4.57 ! [X0 : $tType,X36 : X0,X37 : proces634752977rocess @ X0] : ((proces745025900prefOf @ X0 @ (proces1525233512Action @ X0 @ X36 @ X37)) = X36)),
% 20.81/4.57 file('/export/starexec/sandbox/tmp/tmp.sFYK9PDrEK/DTF2THF_15624.p',fact_27_process_Osel_I1_J)).
% 20.81/4.57 thf(f2734,plain,(
% 20.81/4.57 (a3 = (proces745025900prefOf @ a @ (proces1525233512Action @ a @ a2 @ p2)))),
% 20.81/4.57 inference(superposition,[status(thm)],[f1792,f2444])).
% 20.81/4.57 thf(f2444,plain,(
% 20.81/4.57 ((proces1525233512Action @ a @ a2 @ p2) = (proces1525233512Action @ a @ a3 @ (proces1652378886lution @ b @ a @ sys @ (proces126235999e_CONT @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ (proces1525233512Action @ a @ a3 @ pa))))))),
% 20.81/4.57 inference(forward_demodulation,[status(thm)],[f2442,f1792])).
% 20.81/4.57 thf(f2442,plain,(
% 20.81/4.57 ((proces1525233512Action @ a @ a2 @ p2) = (proces1525233512Action @ a @ (proces745025900prefOf @ a @ (proces1525233512Action @ a @ a3 @ pa)) @ (proces1652378886lution @ b @ a @ sys @ (proces126235999e_CONT @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ (proces1525233512Action @ a @ a3 @ pa))))))),
% 20.81/4.57 inference(backward_demodulation,[status(thm)],[f1659,f2439])).
% 20.81/4.57 thf(f2439,plain,(
% 20.81/4.57 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : proces634752977rocess @ X2,X4 : X1 > proces554692349s_term @ X2 @ X0] : (((proces1708129104e_PREF @ X1 @ X2 @ X0 @ X4 @ (proces1062592052s_PROC @ X2 @ X1 @ X3)) = (proces745025900prefOf @ X2 @ X3))) )),
% 20.81/4.57 inference(equality_proxy_clausification,[status(thm)],[f2438])).
% 20.81/4.57 thf(f2438,plain,(
% 20.81/4.57 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : proces634752977rocess @ X2,X4 : X1 > proces554692349s_term @ X2 @ X0] : ((((proces745025900prefOf @ X2 @ X3) = (proces1708129104e_PREF @ X1 @ X2 @ X0 @ X4 @ (proces1062592052s_PROC @ X2 @ X1 @ X3))) = $true)) )),
% 20.81/4.57 inference(beta_eta_normalization,[status(thm)],[f2437])).
% 20.81/4.57 thf(f2437,plain,(
% 20.81/4.57 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : proces634752977rocess @ X2,X4 : X1 > proces554692349s_term @ X2 @ X0] : (($true = ((^[Y0 : X1 > proces554692349s_term @ X2 @ X0]: ((proces745025900prefOf @ X2 @ X3) = (proces1708129104e_PREF @ X1 @ X2 @ X0 @ Y0 @ (proces1062592052s_PROC @ X2 @ X1 @ X3)))) @ X4))) )),
% 20.81/4.57 inference(pi_clausification,[status(thm)],[f2433])).
% 20.81/4.57 thf(f2433,plain,(
% 20.81/4.57 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : proces634752977rocess @ X2] : (($true = (!! @ (X1 > proces554692349s_term @ X2 @ X0) @ (^[Y0 : X1 > proces554692349s_term @ X2 @ X0]: ((proces745025900prefOf @ X2 @ X3) = (proces1708129104e_PREF @ X1 @ X2 @ X0 @ Y0 @ (proces1062592052s_PROC @ X2 @ X1 @ X3))))))) )),
% 20.81/4.57 inference(beta_eta_normalization,[status(thm)],[f2432])).
% 20.81/4.57 thf(f2432,plain,(
% 20.81/4.57 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : proces634752977rocess @ X2] : (($true = ((^[Y0 : proces634752977rocess @ X2]: (!! @ (X1 > proces554692349s_term @ X2 @ X0) @ (^[Y1 : X1 > proces554692349s_term @ X2 @ X0]: ((proces745025900prefOf @ X2 @ Y0) = (proces1708129104e_PREF @ X1 @ X2 @ X0 @ Y1 @ (proces1062592052s_PROC @ X2 @ X1 @ Y0)))))) @ X3))) )),
% 20.81/4.57 inference(pi_clausification,[status(thm)],[f1439])).
% 20.81/4.57 thf(f1439,plain,(
% 20.81/4.57 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true = (!! @ proces634752977rocess @ X2 @ (^[Y0 : proces634752977rocess @ X2]: (!! @ (X1 > proces554692349s_term @ X2 @ X0) @ (^[Y1 : X1 > proces554692349s_term @ X2 @ X0]: ((proces745025900prefOf @ X2 @ Y0) = (proces1708129104e_PREF @ X1 @ X2 @ X0 @ Y1 @ (proces1062592052s_PROC @ X2 @ X1 @ Y0))))))))) )),
% 20.81/4.57 inference(cnf_transformation,[status(thm)],[f1237])).
% 20.81/4.57 thf(f1237,plain,(
% 20.81/4.57 ! [X0 : $tType,X1 : $tType,X2 : $tType] : ($true = (!! @ proces634752977rocess @ X2 @ (^[Y0 : proces634752977rocess @ X2]: (!! @ (X1 > proces554692349s_term @ X2 @ X0) @ (^[Y1 : X1 > proces554692349s_term @ X2 @ X0]: ((proces745025900prefOf @ X2 @ Y0) = (proces1708129104e_PREF @ X1 @ X2 @ X0 @ Y1 @ (proces1062592052s_PROC @ X2 @ X1 @ Y0))))))))),
% 20.81/4.57 inference(rectify,[status(thm)],[f787])).
% 20.81/4.57 thf(f787,plain,(
% 20.81/4.57 ! [X2 : $tType,X1 : $tType,X0 : $tType] : ($true = (!! @ proces634752977rocess @ X0 @ (^[Y0 : proces634752977rocess @ X0]: (!! @ (X1 > proces554692349s_term @ X0 @ X2) @ (^[Y1 : X1 > proces554692349s_term @ X0 @ X2]: ((proces745025900prefOf @ X0 @ Y0) = (proces1708129104e_PREF @ X1 @ X0 @ X2 @ Y1 @ (proces1062592052s_PROC @ X0 @ X1 @ Y0))))))))),
% 20.81/4.57 inference(closure,[status(thm)],[f786])).
% 20.81/4.57 thf(f786,plain,(
% 20.81/4.57 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true = (!! @ proces634752977rocess @ X0 @ (^[Y0 : proces634752977rocess @ X0]: (!! @ (X1 > proces554692349s_term @ X0 @ X2) @ (^[Y1 : X1 > proces554692349s_term @ X0 @ X2]: ((proces745025900prefOf @ X0 @ Y0) = (proces1708129104e_PREF @ X1 @ X0 @ X2 @ Y1 @ (proces1062592052s_PROC @ X0 @ X1 @ Y0))))))))) )),
% 20.81/4.57 inference(rectify,[status(thm)],[f275])).
% 20.81/4.57 thf(f275,plain,(
% 20.81/4.57 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (((!! @ proces634752977rocess @ X2 @ (^[Y0 : proces634752977rocess @ X2]: (!! @ (X0 > proces554692349s_term @ X2 @ X1) @ (^[Y1 : X0 > proces554692349s_term @ X2 @ X1]: ((proces745025900prefOf @ X2 @ Y0) = (proces1708129104e_PREF @ X0 @ X2 @ X1 @ Y1 @ (proces1062592052s_PROC @ X2 @ X0 @ Y0))))))) = $true)) )),
% 20.81/4.57 inference(fool_elimination,[status(thm)],[f274])).
% 20.81/4.57 thf(f274,plain,(
% 20.81/4.57 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X0 > proces554692349s_term @ X2 @ X1,X4 : proces634752977rocess @ X2] : ((proces745025900prefOf @ X2 @ X4) = (proces1708129104e_PREF @ X0 @ X2 @ X1 @ X3 @ (proces1062592052s_PROC @ X2 @ X0 @ X4)))),
% 20.81/4.57 inference(rectify,[status(thm)],[f14])).
% 20.81/4.57 thf(f14,axiom,(
% 20.81/4.57 ! [X0 : $tType,X1 : $tType,X2 : $tType,X25 : X0 > proces554692349s_term @ X2 @ X1,X27 : proces634752977rocess @ X2] : ((proces1708129104e_PREF @ X0 @ X2 @ X1 @ X25 @ (proces1062592052s_PROC @ X2 @ X0 @ X27)) = (proces745025900prefOf @ X2 @ X27))),
% 20.81/4.57 file('/export/starexec/sandbox/tmp/tmp.sFYK9PDrEK/DTF2THF_15624.p',fact_13_PREF_Osimps_I2_J)).
% 20.81/4.57 thf(f1659,plain,(
% 20.81/4.57 ((proces1525233512Action @ a @ a2 @ p2) = (proces1525233512Action @ a @ (proces1708129104e_PREF @ b @ a @ b @ sys @ (proces1062592052s_PROC @ a @ b @ (proces1525233512Action @ a @ a3 @ pa))) @ (proces1652378886lution @ b @ a @ sys @ (proces126235999e_CONT @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ (proces1525233512Action @ a @ a3 @ pa))))))),
% 20.81/4.57 inference(forward_demodulation,[status(thm)],[f1635,f1530])).
% 20.81/4.57 thf(f1530,plain,(
% 20.81/4.57 ((proces1525233512Action @ a @ a2 @ p2) = (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ (proces1525233512Action @ a @ a3 @ pa))))),
% 20.81/4.57 inference(cnf_transformation,[status(thm)],[f276])).
% 20.81/4.57 thf(f276,plain,(
% 20.81/4.57 ((proces1525233512Action @ a @ a2 @ p2) = (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ (proces1525233512Action @ a @ a3 @ pa))))),
% 20.81/4.57 inference(fool_elimination,[status(thm)],[f3])).
% 20.81/4.57 thf(f3,axiom,(
% 20.81/4.57 ((proces1525233512Action @ a @ a2 @ p2) = (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ (proces1525233512Action @ a @ a3 @ pa))))),
% 20.81/4.57 file('/export/starexec/sandbox/tmp/tmp.sFYK9PDrEK/DTF2THF_15624.p',fact_2_Action)).
% 20.81/4.57 thf(f1635,plain,(
% 20.81/4.57 ((proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ (proces1525233512Action @ a @ a3 @ pa))) = (proces1525233512Action @ a @ (proces1708129104e_PREF @ b @ a @ b @ sys @ (proces1062592052s_PROC @ a @ b @ (proces1525233512Action @ a @ a3 @ pa))) @ (proces1652378886lution @ b @ a @ sys @ (proces126235999e_CONT @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ (proces1525233512Action @ a @ a3 @ pa))))))),
% 20.81/4.57 inference(cnf_transformation,[status(thm)],[f336])).
% 20.81/4.57 thf(f336,plain,(
% 20.81/4.57 ((proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ (proces1525233512Action @ a @ a3 @ pa))) = (proces1525233512Action @ a @ (proces1708129104e_PREF @ b @ a @ b @ sys @ (proces1062592052s_PROC @ a @ b @ (proces1525233512Action @ a @ a3 @ pa))) @ (proces1652378886lution @ b @ a @ sys @ (proces126235999e_CONT @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ (proces1525233512Action @ a @ a3 @ pa))))))),
% 20.81/4.57 inference(fool_elimination,[status(thm)],[f5])).
% 20.81/4.57 thf(f5,axiom,(
% 20.81/4.57 ((proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ (proces1525233512Action @ a @ a3 @ pa))) = (proces1525233512Action @ a @ (proces1708129104e_PREF @ b @ a @ b @ sys @ (proces1062592052s_PROC @ a @ b @ (proces1525233512Action @ a @ a3 @ pa))) @ (proces1652378886lution @ b @ a @ sys @ (proces126235999e_CONT @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ (proces1525233512Action @ a @ a3 @ pa))))))),
% 20.81/4.57 file('/export/starexec/sandbox/tmp/tmp.sFYK9PDrEK/DTF2THF_15624.p',fact_4__092_060open_062solution_Asys_A_IPROC_A_IAction_Aa_Ap_J_J_A_061_AAction_A_IPREF_Asys_A_IPROC_A_IAction_Aa_Ap_J_J_J_A_Isolution_Asys_A_ICONT_Asys_A_IPROC_A_IAction_Aa_Ap_J_J_J_J_092_060close_062)).
% 20.81/4.57 thf(f2751,plain,(
% 20.81/4.57 (p2 = (proces1652378886lution @ b @ a @ sys @ (proces126235999e_CONT @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ (proces1525233512Action @ a @ a3 @ pa)))))),
% 20.81/4.57 inference(forward_demodulation,[status(thm)],[f2735,f1806])).
% 20.81/4.57 thf(f2735,plain,(
% 20.81/4.57 ((proces1652378886lution @ b @ a @ sys @ (proces126235999e_CONT @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ (proces1525233512Action @ a @ a3 @ pa)))) = (proces1778668539contOf @ a @ (proces1525233512Action @ a @ a2 @ p2)))),
% 20.81/4.57 inference(superposition,[status(thm)],[f1806,f2444])).
% 20.81/4.57 thf(f2759,plain,(
% 20.81/4.57 spl0_1),
% 20.81/4.57 inference(avatar_split_clause,[status(thm)],[f2758,f2107])).
% 20.81/4.57 thf(f2758,plain,(
% 20.81/4.57 ($false = (p2 = (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa))))),
% 20.81/4.57 inference(boolean_simplification,[status(thm)],[f2757])).
% 20.81/4.57 thf(f2757,plain,(
% 20.81/4.57 ($false = ($true & (p2 = (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa)))))),
% 20.81/4.57 inference(boolean_simplification,[status(thm)],[f2753])).
% 20.81/4.57 thf(f2753,plain,(
% 20.81/4.57 ($false = ((a2 = a2) & (p2 = (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa)))))),
% 20.81/4.57 inference(backward_demodulation,[status(thm)],[f2102,f2748])).
% 20.81/4.57 thf(f2102,plain,(
% 20.81/4.57 (((a2 = a3) & (p2 = (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa)))) = $false)),
% 20.81/4.57 inference(not_proxy_clausification,[status(thm)],[f1547])).
% 20.81/4.57 thf(f1547,plain,(
% 20.81/4.57 ((~ ((a2 = a3) & (p2 = (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa))))) = $true)),
% 20.81/4.57 inference(cnf_transformation,[status(thm)],[f699])).
% 20.81/4.57 thf(f699,plain,(
% 20.81/4.57 ((~ ((a2 = a3) & (p2 = (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa))))) = $true)),
% 20.81/4.57 inference(fool_elimination,[status(thm)],[f260])).
% 20.81/4.57 thf(f260,negated_conjecture,(
% 20.81/4.57 ~((p2 = (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa))) & (a2 = a3))),
% 20.81/4.57 inference(negated_conjecture,[status(cth)],[f259])).
% 20.81/4.57 thf(f259,conjecture,(
% 20.81/4.57 (p2 = (proces1652378886lution @ b @ a @ sys @ (proces1062592052s_PROC @ a @ b @ pa))) & (a2 = a3)),
% 20.81/4.57 file('/export/starexec/sandbox/tmp/tmp.sFYK9PDrEK/DTF2THF_15624.p',conj_0)).
% 20.81/4.57 % SZS output end Proof for DTF2THF_15624
% 20.81/4.57 % (15821)------------------------------
% 20.81/4.57 % (15821)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.81/4.57 % (15821)Termination reason: Refutation
% 20.81/4.57
% 20.81/4.57 % (15821)Memory used [KB]: 13432
% 20.81/4.57 % (15821)Time elapsed: 1.263 s
% 20.81/4.57 % (15821)Instructions burned: 2588 (million)
% 20.81/4.57 % (15821)------------------------------
% 20.81/4.57 % (15821)------------------------------
% 20.81/4.57 % (15722)Success in time 2.701 s
%------------------------------------------------------------------------------